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": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.793. | {
"id": "WUA_STAT_25K_010701",
"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]=2.16; Var[X]=1.382. | {
"id": "WUA_STAT_25K_010702",
"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=10.04, μ=29.24, σ=23... | z = -0.821. | {
"id": "WUA_STAT_25K_010703",
"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]=10.56; Var[X]=5.914. | {
"id": "WUA_STAT_25K_010704",
"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=59.93, μ=64.34, σ=4.... | z = -1.070. | {
"id": "WUA_STAT_25K_010705",
"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 ≈ [115.09, 126.87]. | {
"id": "WUA_STAT_25K_010706",
"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]=4.68; Var[X]=2.995. | {
"id": "WUA_STAT_25K_010707",
"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": "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_010708",
"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": "Compute z=(x-μ)/σ. Given x=42.01, μ=95.49, σ=8.... | z = -6.359. | {
"id": "WUA_STAT_25K_010709",
"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=7... | 95% CI ≈ [74.88, 75.76]. | {
"id": "WUA_STAT_25K_010710",
"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=2... | 95% CI ≈ [23.21, 31.01]. | {
"id": "WUA_STAT_25K_010711",
"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]=13.72; Var[X]=6.997. | {
"id": "WUA_STAT_25K_010712",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=18.20; Var[X]=6.370. | {
"id": "WUA_STAT_25K_010713",
"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=26.86, μ=56.05, σ=19... | z = -1.462. | {
"id": "WUA_STAT_25K_010714",
"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=43.38, μ=21.05, σ=24... | z = 0.901. | {
"id": "WUA_STAT_25K_010715",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=5.28; Var[X]=4.435. | {
"id": "WUA_STAT_25K_010716",
"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 ≈ [137.03, 148.95]. | {
"id": "WUA_STAT_25K_010717",
"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=2... | 95% CI ≈ [17.07, 34.85]. | {
"id": "WUA_STAT_25K_010718",
"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=7... | 95% CI ≈ [75.45, 81.79]. | {
"id": "WUA_STAT_25K_010719",
"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]=8.97; Var[X]=6.907. | {
"id": "WUA_STAT_25K_010720",
"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=3... | 95% CI ≈ [33.79, 43.45]. | {
"id": "WUA_STAT_25K_010721",
"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]=27.75; Var[X]=6.938. | {
"id": "WUA_STAT_25K_010722",
"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 ≈ 0.487. | {
"id": "WUA_STAT_25K_010723",
"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 ≈ 0.508. | {
"id": "WUA_STAT_25K_010724",
"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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"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=5... | 95% CI ≈ [54.88, 60.74]. | {
"id": "WUA_STAT_25K_010725",
"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"... | [
{
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"evidence_type": "self_contained",
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}
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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=36.86, μ=9.58, σ=9.4... | z = 2.881. | {
"id": "WUA_STAT_25K_010726",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=1.32; Var[X]=1.162. | {
"id": "WUA_STAT_25K_010727",
"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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=9... | 95% CI ≈ [96.07, 100.91]. | {
"id": "WUA_STAT_25K_010728",
"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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} |
{
"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 ≈ [175.80, 190.36]. | {
"id": "WUA_STAT_25K_010729",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=0.77; Var[X]=0.716. | {
"id": "WUA_STAT_25K_010730",
"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=75.56, μ=0.7, σ=22.0... | z = 3.392. | {
"id": "WUA_STAT_25K_010731",
"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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"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 ≈ [116.89, 123.13]. | {
"id": "WUA_STAT_25K_010732",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=24.70; Var[X]=8.645. | {
"id": "WUA_STAT_25K_010733",
"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=1.76, μ=37.72, σ=18.... | z = -1.955. | {
"id": "WUA_STAT_25K_010734",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=2.40; Var[X]=1.248. | {
"id": "WUA_STAT_25K_010735",
"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 ≈ 0.842. | {
"id": "WUA_STAT_25K_010736",
"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=5... | 95% CI ≈ [49.60, 59.76]. | {
"id": "WUA_STAT_25K_010737",
"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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"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 ≈ [112.67, 115.61]. | {
"id": "WUA_STAT_25K_010738",
"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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [166.85, 180.77]. | {
"id": "WUA_STAT_25K_010739",
"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 ≈ [190.60, 203.52]. | {
"id": "WUA_STAT_25K_010740",
"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": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.365. | {
"id": "WUA_STAT_25K_010741",
"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]=2.10; Var[X]=1.470. | {
"id": "WUA_STAT_25K_010742",
"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 ≈ [123.54, 146.44]. | {
"id": "WUA_STAT_25K_010743",
"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]=3.24; Var[X]=2.948. | {
"id": "WUA_STAT_25K_010744",
"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 ≈ 0.438. | {
"id": "WUA_STAT_25K_010745",
"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=65.12, μ=6.31, σ=1.1... | z = 50.265. | {
"id": "WUA_STAT_25K_010746",
"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": "Compute z=(x-μ)/σ. Given x=87.13, μ=78.29, σ=23... | z = 0.381. | {
"id": "WUA_STAT_25K_010747",
"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]=4.16; Var[X]=2.829. | {
"id": "WUA_STAT_25K_010748",
"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... | [
{
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"source_url": "",
"evidence_type": "self_contained",
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}
] | {
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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=61.27, μ=45.32, σ=13... | z = 1.180. | {
"id": "WUA_STAT_25K_010749",
"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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} |
{
"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 ≈ 0.186. | {
"id": "WUA_STAT_25K_010750",
"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": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.583. | {
"id": "WUA_STAT_25K_010751",
"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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [174.45, 183.99]. | {
"id": "WUA_STAT_25K_010752",
"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=54.55, μ=48.74, σ=22... | z = 0.258. | {
"id": "WUA_STAT_25K_010753",
"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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [193.66, 196.06]. | {
"id": "WUA_STAT_25K_010754",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=12.73; Var[X]=4.201. | {
"id": "WUA_STAT_25K_010755",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=21.28; Var[X]=9.363. | {
"id": "WUA_STAT_25K_010756",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=2.52; Var[X]=1.991. | {
"id": "WUA_STAT_25K_010757",
"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 ≈ [3.04, 25.78]. | {
"id": "WUA_STAT_25K_010758",
"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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"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]=1.26; Var[X]=1.084. | {
"id": "WUA_STAT_25K_010759",
"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=78.52, μ=93.18, σ=22... | z = -0.650. | {
"id": "WUA_STAT_25K_010760",
"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 ≈ 0.157. | {
"id": "WUA_STAT_25K_010761",
"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 ≈ [130.09, 133.93]. | {
"id": "WUA_STAT_25K_010762",
"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": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.497. | {
"id": "WUA_STAT_25K_010763",
"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=6... | 95% CI ≈ [60.22, 68.44]. | {
"id": "WUA_STAT_25K_010764",
"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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{
"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=53.29, μ=10.38, σ=17... | z = 2.453. | {
"id": "WUA_STAT_25K_010765",
"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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"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=33.8, μ=79.86, σ=20.... | z = -2.236. | {
"id": "WUA_STAT_25K_010766",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=16.92; Var[X]=8.968. | {
"id": "WUA_STAT_25K_010767",
"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 ≈ [-0.41, 29.35]. | {
"id": "WUA_STAT_25K_010768",
"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]=7.65; Var[X]=4.208. | {
"id": "WUA_STAT_25K_010769",
"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 ≈ [143.64, 179.12]. | {
"id": "WUA_STAT_25K_010770",
"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=58.22, μ=57.95, σ=15... | z = 0.017. | {
"id": "WUA_STAT_25K_010771",
"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]=17.28; Var[X]=7.949. | {
"id": "WUA_STAT_25K_010772",
"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 ≈ 0.304. | {
"id": "WUA_STAT_25K_010773",
"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=2... | 95% CI ≈ [20.71, 27.23]. | {
"id": "WUA_STAT_25K_010774",
"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]=25.08; Var[X]=8.527. | {
"id": "WUA_STAT_25K_010775",
"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=2... | 95% CI ≈ [22.78, 32.32]. | {
"id": "WUA_STAT_25K_010776",
"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]=4.96; Var[X]=3.422. | {
"id": "WUA_STAT_25K_010777",
"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 ≈ 0.593. | {
"id": "WUA_STAT_25K_010778",
"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=99.5, μ=62.89, σ=13.... | z = 2.782. | {
"id": "WUA_STAT_25K_010779",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=6.12; Var[X]=1.958. | {
"id": "WUA_STAT_25K_010780",
"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": "Compute z=(x-μ)/σ. Given x=17.77, μ=85.97, σ=6.... | z = -10.365. | {
"id": "WUA_STAT_25K_010781",
"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 ≈ [160.73, 186.99]. | {
"id": "WUA_STAT_25K_010782",
"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=9... | 95% CI ≈ [94.92, 99.42]. | {
"id": "WUA_STAT_25K_010783",
"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=71.18, μ=27.54, σ=4.... | z = 10.390. | {
"id": "WUA_STAT_25K_010784",
"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=23.13, μ=79.12, σ=21... | z = -2.561. | {
"id": "WUA_STAT_25K_010785",
"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=1.68, μ=95.71, σ=20.... | z = -4.632. | {
"id": "WUA_STAT_25K_010786",
"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 ≈ 0.250. | {
"id": "WUA_STAT_25K_010787",
"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=11.13, μ=64.75, σ=18... | z = -2.833. | {
"id": "WUA_STAT_25K_010788",
"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=24.99, μ=79.0, σ=14.... | z = -3.699. | {
"id": "WUA_STAT_25K_010789",
"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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"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]=6.63; Var[X]=5.503. | {
"id": "WUA_STAT_25K_010790",
"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 ≈ 0.968. | {
"id": "WUA_STAT_25K_010791",
"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 ≈ 0.754. | {
"id": "WUA_STAT_25K_010792",
"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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} |
{
"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]=10.44; Var[X]=7.412. | {
"id": "WUA_STAT_25K_010793",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=5.06; Var[X]=2.732. | {
"id": "WUA_STAT_25K_010794",
"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",
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"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=87.69, μ=42.44, σ=17... | z = 2.545. | {
"id": "WUA_STAT_25K_010795",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
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"... | [
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},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=7... | 95% CI ≈ [69.08, 78.04]. | {
"id": "WUA_STAT_25K_010796",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
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... | [
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},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [142.46, 148.20]. | {
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"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
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"license": "cc-by-4.... | [
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"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 ≈ 0.380. | {
"id": "WUA_STAT_25K_010798",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
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... | [
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"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=51.31, μ=83.16, σ=6.... | z = -4.643. | {
"id": "WUA_STAT_25K_010799",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
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"... | [
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},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.367. | {
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"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
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... | [
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