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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [6.18, 16.26]. | {
"id": "WUA_STAT_25K_012101",
"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]=30.40; Var[X]=7.296. | {
"id": "WUA_STAT_25K_012102",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=12.48; Var[X]=8.486. | {
"id": "WUA_STAT_25K_012103",
"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": "Compute z=(x-μ)/σ. Given x=93.43, μ=94.33, σ=1.... | z = -0.882. | {
"id": "WUA_STAT_25K_012104",
"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=54.64, μ=64.69, σ=9.... | z = -1.098. | {
"id": "WUA_STAT_25K_012105",
"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=9... | 95% CI ≈ [87.13, 101.33]. | {
"id": "WUA_STAT_25K_012106",
"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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [189.70, 194.40]. | {
"id": "WUA_STAT_25K_012107",
"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=10.1, μ=28.67, σ=1.1... | z = -16.289. | {
"id": "WUA_STAT_25K_012108",
"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 ≈ [169.97, 174.61]. | {
"id": "WUA_STAT_25K_012109",
"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 ≈ [164.90, 168.64]. | {
"id": "WUA_STAT_25K_012110",
"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=71.21, μ=77.46, σ=24... | z = -0.259. | {
"id": "WUA_STAT_25K_012111",
"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=67.59, μ=14.99, σ=19... | z = 2.692. | {
"id": "WUA_STAT_25K_012112",
"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]=3.04; Var[X]=1.885. | {
"id": "WUA_STAT_25K_012113",
"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 ≈ 0.501. | {
"id": "WUA_STAT_25K_012114",
"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]=4.20; Var[X]=2.730. | {
"id": "WUA_STAT_25K_012115",
"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 ≈ 0.706. | {
"id": "WUA_STAT_25K_012116",
"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=9... | 95% CI ≈ [94.39, 95.69]. | {
"id": "WUA_STAT_25K_012117",
"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]=18.24; Var[X]=7.843. | {
"id": "WUA_STAT_25K_012118",
"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=7... | 95% CI ≈ [70.67, 72.59]. | {
"id": "WUA_STAT_25K_012119",
"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 ≈ 0.737. | {
"id": "WUA_STAT_25K_012120",
"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=29.89, μ=41.1, σ=24.... | z = -0.461. | {
"id": "WUA_STAT_25K_012121",
"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]=7.00; Var[X]=5.250. | {
"id": "WUA_STAT_25K_012122",
"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": "Compute z=(x-μ)/σ. Given x=48.46, μ=16.96, σ=6.... | z = 5.064. | {
"id": "WUA_STAT_25K_012123",
"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]=7.59; Var[X]=2.353. | {
"id": "WUA_STAT_25K_012124",
"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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{
"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 ≈ [20.55, 27.41]. | {
"id": "WUA_STAT_25K_012125",
"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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{
"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]=3.20; Var[X]=2.176. | {
"id": "WUA_STAT_25K_012126",
"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",
"... | [
{
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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=74.82, μ=44.59, σ=24... | z = 1.238. | {
"id": "WUA_STAT_25K_012127",
"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]=21.45; Var[X]=9.652. | {
"id": "WUA_STAT_25K_012128",
"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=85.8, μ=13.97, σ=12.... | z = 5.678. | {
"id": "WUA_STAT_25K_012129",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=9.03; Var[X]=5.147. | {
"id": "WUA_STAT_25K_012130",
"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=5.15, μ=48.49, σ=14.... | z = -2.956. | {
"id": "WUA_STAT_25K_012131",
"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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [156.85, 165.21]. | {
"id": "WUA_STAT_25K_012132",
"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 ≈ [156.78, 175.76]. | {
"id": "WUA_STAT_25K_012133",
"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 ≈ 0.798. | {
"id": "WUA_STAT_25K_012134",
"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]=1.14; Var[X]=0.923. | {
"id": "WUA_STAT_25K_012135",
"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=24.36, μ=25.58, σ=13... | z = -0.093. | {
"id": "WUA_STAT_25K_012136",
"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=52.33, μ=34.4, σ=24.... | z = 0.729. | {
"id": "WUA_STAT_25K_012137",
"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 ≈ [171.86, 193.02]. | {
"id": "WUA_STAT_25K_012138",
"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=8.42, μ=45.51, σ=22.... | z = -1.653. | {
"id": "WUA_STAT_25K_012139",
"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=58.96, μ=81.87, σ=8.... | z = -2.825. | {
"id": "WUA_STAT_25K_012140",
"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]=3.45; Var[X]=1.070. | {
"id": "WUA_STAT_25K_012141",
"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": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.487. | {
"id": "WUA_STAT_25K_012142",
"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": "Compute z=(x-μ)/σ. Given x=25.95, μ=18.63, σ=18... | z = 0.387. | {
"id": "WUA_STAT_25K_012143",
"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": "Compute z=(x-μ)/σ. Given x=12.99, μ=61.35, σ=3.... | z = -12.828. | {
"id": "WUA_STAT_25K_012144",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=11.16; Var[X]=7.700. | {
"id": "WUA_STAT_25K_012145",
"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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=4... | 95% CI ≈ [31.35, 48.73]. | {
"id": "WUA_STAT_25K_012146",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=6.72; Var[X]=3.494. | {
"id": "WUA_STAT_25K_012147",
"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": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.216. | {
"id": "WUA_STAT_25K_012148",
"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 ≈ [172.78, 177.44]. | {
"id": "WUA_STAT_25K_012149",
"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 ≈ [120.19, 128.39]. | {
"id": "WUA_STAT_25K_012150",
"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 ≈ 0.903. | {
"id": "WUA_STAT_25K_012151",
"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 ≈ 0.139. | {
"id": "WUA_STAT_25K_012152",
"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=24.72, μ=25.59, σ=22... | z = -0.039. | {
"id": "WUA_STAT_25K_012153",
"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=57.73, μ=46.86, σ=14... | z = 0.744. | {
"id": "WUA_STAT_25K_012154",
"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=67.08, μ=14.9, σ=2.9... | z = 17.870. | {
"id": "WUA_STAT_25K_012155",
"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]=3.99; Var[X]=1.716. | {
"id": "WUA_STAT_25K_012156",
"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 ≈ 0.485. | {
"id": "WUA_STAT_25K_012157",
"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=39.44, μ=86.8, σ=8.4... | z = -5.598. | {
"id": "WUA_STAT_25K_012158",
"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=60.6, μ=37.67, σ=5.7... | z = 3.988. | {
"id": "WUA_STAT_25K_012159",
"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=9... | 95% CI ≈ [98.51, 99.81]. | {
"id": "WUA_STAT_25K_012160",
"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 ≈ 0.070. | {
"id": "WUA_STAT_25K_012161",
"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=31.2, μ=4.35, σ=13.8... | z = 1.946. | {
"id": "WUA_STAT_25K_012162",
"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 ≈ 0.602. | {
"id": "WUA_STAT_25K_012163",
"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]=24.42; Var[X]=8.303. | {
"id": "WUA_STAT_25K_012164",
"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]=1.61; Var[X]=1.497. | {
"id": "WUA_STAT_25K_012165",
"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 ≈ [110.59, 136.87]. | {
"id": "WUA_STAT_25K_012166",
"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]=9.88; Var[X]=4.742. | {
"id": "WUA_STAT_25K_012167",
"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 ≈ 0.727. | {
"id": "WUA_STAT_25K_012168",
"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": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.378. | {
"id": "WUA_STAT_25K_012169",
"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=29.72, μ=12.85, σ=16... | z = 0.998. | {
"id": "WUA_STAT_25K_012170",
"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=96.03, μ=72.62, σ=6.... | z = 3.590. | {
"id": "WUA_STAT_25K_012171",
"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 ≈ [163.42, 178.22]. | {
"id": "WUA_STAT_25K_012172",
"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 ≈ [180.92, 198.30]. | {
"id": "WUA_STAT_25K_012173",
"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=5... | 95% CI ≈ [44.33, 59.91]. | {
"id": "WUA_STAT_25K_012174",
"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": "Compute z=(x-μ)/σ. Given x=42.06, μ=83.96, σ=13... | z = -3.150. | {
"id": "WUA_STAT_25K_012175",
"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 ≈ 0.240. | {
"id": "WUA_STAT_25K_012176",
"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 ≈ [183.96, 189.56]. | {
"id": "WUA_STAT_25K_012177",
"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=45.76, μ=25.35, σ=8.... | z = 2.483. | {
"id": "WUA_STAT_25K_012178",
"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]=4.02; Var[X]=1.327. | {
"id": "WUA_STAT_25K_012179",
"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 ≈ 0.402. | {
"id": "WUA_STAT_25K_012180",
"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=7... | 95% CI ≈ [66.39, 82.51]. | {
"id": "WUA_STAT_25K_012181",
"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 ≈ [172.51, 181.39]. | {
"id": "WUA_STAT_25K_012182",
"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 ≈ [111.83, 115.47]. | {
"id": "WUA_STAT_25K_012183",
"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 ≈ [126.79, 145.19]. | {
"id": "WUA_STAT_25K_012184",
"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=73.65, μ=43.31, σ=16... | z = 1.801. | {
"id": "WUA_STAT_25K_012185",
"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 ≈ 0.204. | {
"id": "WUA_STAT_25K_012186",
"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=53.93, μ=17.77, σ=21... | z = 1.688. | {
"id": "WUA_STAT_25K_012187",
"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 ≈ 0.510. | {
"id": "WUA_STAT_25K_012188",
"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 ≈ [180.53, 194.23]. | {
"id": "WUA_STAT_25K_012189",
"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 ≈ [97.70, 99.36]. | {
"id": "WUA_STAT_25K_012190",
"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 ≈ 0.323. | {
"id": "WUA_STAT_25K_012191",
"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 ≈ [94.46, 107.08]. | {
"id": "WUA_STAT_25K_012192",
"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=29.25, μ=13.02, σ=1.... | z = 15.457. | {
"id": "WUA_STAT_25K_012193",
"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=6... | 95% CI ≈ [64.36, 72.10]. | {
"id": "WUA_STAT_25K_012194",
"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 ≈ 0.084. | {
"id": "WUA_STAT_25K_012195",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
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"license": "cc-by-4.0",
"tags": [
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},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=5.32; Var[X]=3.298. | {
"id": "WUA_STAT_25K_012196",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
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"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=56.02, μ=72.54, σ=4.... | z = -3.615. | {
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},
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"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=7... | 95% CI ≈ [71.23, 83.51]. | {
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"subdomain": "stats_math::confidence_intervals",
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},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [144.40, 167.04]. | {
"id": "WUA_STAT_25K_012199",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
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},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [162.60, 172.52]. | {
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"subdomain": "stats_math::confidence_intervals",
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