prompt dict | response string | meta dict | fact_sources list | artifacts dict |
|---|---|---|---|---|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=4.72; Var[X]=1.935. | {
"id": "WUA_STAT_25K_014201",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=42.54, μ=47.43, σ=10... | z = -0.452. | {
"id": "WUA_STAT_25K_014202",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.825. | {
"id": "WUA_STAT_25K_014203",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=99.11, μ=57.32, σ=3.... | z = 10.474. | {
"id": "WUA_STAT_25K_014204",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=40.42, μ=59.86, σ=3.... | z = -6.480. | {
"id": "WUA_STAT_25K_014205",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.086. | {
"id": "WUA_STAT_25K_014206",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=2.73; Var[X]=1.665. | {
"id": "WUA_STAT_25K_014207",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [110.22, 117.88]. | {
"id": "WUA_STAT_25K_014208",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.120. | {
"id": "WUA_STAT_25K_014209",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=7... | 95% CI ≈ [71.17, 75.39]. | {
"id": "WUA_STAT_25K_014210",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=2.68, μ=28.35, σ=22.... | z = -1.148. | {
"id": "WUA_STAT_25K_014211",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=24.82; Var[X]=6.701. | {
"id": "WUA_STAT_25K_014212",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.620. | {
"id": "WUA_STAT_25K_014213",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=12.64; Var[X]=2.654. | {
"id": "WUA_STAT_25K_014214",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.576. | {
"id": "WUA_STAT_25K_014215",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=12.28, μ=39.61, σ=18... | z = -1.461. | {
"id": "WUA_STAT_25K_014216",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=6.46; Var[X]=4.005. | {
"id": "WUA_STAT_25K_014217",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.256. | {
"id": "WUA_STAT_25K_014218",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [162.38, 168.86]. | {
"id": "WUA_STAT_25K_014219",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=8... | 95% CI ≈ [74.17, 86.37]. | {
"id": "WUA_STAT_25K_014220",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=7.98; Var[X]=4.628. | {
"id": "WUA_STAT_25K_014221",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [0.69, 21.73]. | {
"id": "WUA_STAT_25K_014222",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=28.12; Var[X]=7.311. | {
"id": "WUA_STAT_25K_014223",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.182. | {
"id": "WUA_STAT_25K_014224",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=5.46; Var[X]=4.696. | {
"id": "WUA_STAT_25K_014225",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=56.68, μ=45.46, σ=11... | z = 1.011. | {
"id": "WUA_STAT_25K_014226",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.532. | {
"id": "WUA_STAT_25K_014227",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=49.94, μ=29.39, σ=24... | z = 0.852. | {
"id": "WUA_STAT_25K_014228",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=6.63; Var[X]=4.044. | {
"id": "WUA_STAT_25K_014229",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=4.05, μ=82.92, σ=22.... | z = -3.455. | {
"id": "WUA_STAT_25K_014230",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.655. | {
"id": "WUA_STAT_25K_014231",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=11.70; Var[X]=2.574. | {
"id": "WUA_STAT_25K_014232",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [104.99, 114.75]. | {
"id": "WUA_STAT_25K_014233",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=2.80; Var[X]=2.408. | {
"id": "WUA_STAT_25K_014234",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=75.23, μ=24.52, σ=24... | z = 2.078. | {
"id": "WUA_STAT_25K_014235",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.134. | {
"id": "WUA_STAT_25K_014236",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=42.66, μ=73.67, σ=4.... | z = -7.145. | {
"id": "WUA_STAT_25K_014237",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.648. | {
"id": "WUA_STAT_25K_014238",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=2... | 95% CI ≈ [18.37, 29.01]. | {
"id": "WUA_STAT_25K_014239",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=69.7, μ=40.6, σ=19.9... | z = 1.462. | {
"id": "WUA_STAT_25K_014240",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.546. | {
"id": "WUA_STAT_25K_014241",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=73.91, μ=76.23, σ=5.... | z = -0.451. | {
"id": "WUA_STAT_25K_014242",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.815. | {
"id": "WUA_STAT_25K_014243",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=10.8, μ=59.34, σ=20.... | z = -2.404. | {
"id": "WUA_STAT_25K_014244",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.758. | {
"id": "WUA_STAT_25K_014245",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [132.97, 134.65]. | {
"id": "WUA_STAT_25K_014246",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=4... | 95% CI ≈ [42.26, 49.00]. | {
"id": "WUA_STAT_25K_014247",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=71.8, μ=34.68, σ=6.3... | z = 5.846. | {
"id": "WUA_STAT_25K_014248",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [191.40, 196.18]. | {
"id": "WUA_STAT_25K_014249",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.169. | {
"id": "WUA_STAT_25K_014250",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [130.59, 139.11]. | {
"id": "WUA_STAT_25K_014251",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [14.56, 25.32]. | {
"id": "WUA_STAT_25K_014252",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=39.54, μ=83.52, σ=11... | z = -3.959. | {
"id": "WUA_STAT_25K_014253",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=81.68, μ=71.37, σ=15... | z = 0.687. | {
"id": "WUA_STAT_25K_014254",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=56.63, μ=26.83, σ=12... | z = 2.423. | {
"id": "WUA_STAT_25K_014255",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=3... | 95% CI ≈ [36.99, 39.37]. | {
"id": "WUA_STAT_25K_014256",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.279. | {
"id": "WUA_STAT_25K_014257",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [154.29, 173.45]. | {
"id": "WUA_STAT_25K_014258",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=25.0, μ=13.84, σ=3.2... | z = 3.487. | {
"id": "WUA_STAT_25K_014259",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [180.26, 191.54]. | {
"id": "WUA_STAT_25K_014260",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=83.37, μ=0.68, σ=20.... | z = 3.941. | {
"id": "WUA_STAT_25K_014261",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.168. | {
"id": "WUA_STAT_25K_014262",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=3.84; Var[X]=2.611. | {
"id": "WUA_STAT_25K_014263",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [179.11, 193.37]. | {
"id": "WUA_STAT_25K_014264",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=98.36, μ=57.21, σ=6.... | z = 6.151. | {
"id": "WUA_STAT_25K_014265",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.040. | {
"id": "WUA_STAT_25K_014266",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=9... | 95% CI ≈ [96.31, 101.03]. | {
"id": "WUA_STAT_25K_014267",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=91.2, μ=39.59, σ=24.... | z = 2.101. | {
"id": "WUA_STAT_25K_014268",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [187.50, 192.08]. | {
"id": "WUA_STAT_25K_014269",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=76.64, μ=46.75, σ=19... | z = 1.507. | {
"id": "WUA_STAT_25K_014270",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.243. | {
"id": "WUA_STAT_25K_014271",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=8.55; Var[X]=4.703. | {
"id": "WUA_STAT_25K_014272",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=86.76, μ=53.17, σ=5.... | z = 5.956. | {
"id": "WUA_STAT_25K_014273",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=8... | 95% CI ≈ [81.89, 92.29]. | {
"id": "WUA_STAT_25K_014274",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [7.45, 12.73]. | {
"id": "WUA_STAT_25K_014275",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.485. | {
"id": "WUA_STAT_25K_014276",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.427. | {
"id": "WUA_STAT_25K_014277",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=22.04; Var[X]=9.257. | {
"id": "WUA_STAT_25K_014278",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=97.38, μ=22.24, σ=22... | z = 3.326. | {
"id": "WUA_STAT_25K_014279",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=23.94; Var[X]=8.858. | {
"id": "WUA_STAT_25K_014280",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=26.91; Var[X]=8.342. | {
"id": "WUA_STAT_25K_014281",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.241. | {
"id": "WUA_STAT_25K_014282",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.611. | {
"id": "WUA_STAT_25K_014283",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=74.52, μ=21.04, σ=1.... | z = 37.139. | {
"id": "WUA_STAT_25K_014284",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=4... | 95% CI ≈ [30.18, 53.70]. | {
"id": "WUA_STAT_25K_014285",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=61.95, μ=28.06, σ=13... | z = 2.512. | {
"id": "WUA_STAT_25K_014286",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=76.77, μ=21.44, σ=3.... | z = 15.076. | {
"id": "WUA_STAT_25K_014287",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=84.12, μ=87.71, σ=21... | z = -0.170. | {
"id": "WUA_STAT_25K_014288",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.315. | {
"id": "WUA_STAT_25K_014289",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=82.29, μ=72.47, σ=11... | z = 0.871. | {
"id": "WUA_STAT_25K_014290",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.054. | {
"id": "WUA_STAT_25K_014291",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=22.89, μ=67.6, σ=2.7... | z = -16.258. | {
"id": "WUA_STAT_25K_014292",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [169.48, 178.04]. | {
"id": "WUA_STAT_25K_014293",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=48.07, μ=94.66, σ=17... | z = -2.664. | {
"id": "WUA_STAT_25K_014294",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=93.93, μ=67.56, σ=5.... | z = 4.920. | {
"id": "WUA_STAT_25K_014295",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.514. | {
"id": "WUA_STAT_25K_014296",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=7.10; Var[X]=2.059. | {
"id": "WUA_STAT_25K_014297",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.797. | {
"id": "WUA_STAT_25K_014298",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=37.61, μ=37.73, σ=24... | z = -0.005. | {
"id": "WUA_STAT_25K_014299",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [166.82, 196.46]. | {
"id": "WUA_STAT_25K_014300",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
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