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 ≈ 0.170. | {
"id": "WUA_STAT_25K_015901",
"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 ≈ 0.371. | {
"id": "WUA_STAT_25K_015902",
"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=3... | 95% CI ≈ [26.58, 35.68]. | {
"id": "WUA_STAT_25K_015903",
"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=3... | 95% CI ≈ [23.50, 37.82]. | {
"id": "WUA_STAT_25K_015904",
"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=4... | 95% CI ≈ [43.15, 45.91]. | {
"id": "WUA_STAT_25K_015905",
"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=7.93, μ=0.04, σ=14.2... | z = 0.553. | {
"id": "WUA_STAT_25K_015906",
"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 ≈ 0.256. | {
"id": "WUA_STAT_25K_015907",
"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 ≈ [155.38, 163.18]. | {
"id": "WUA_STAT_25K_015908",
"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]=1.43; Var[X]=1.273. | {
"id": "WUA_STAT_25K_015909",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=5.28; Var[X]=3.538. | {
"id": "WUA_STAT_25K_015910",
"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=10.52, μ=98.69, σ=14... | z = -5.965. | {
"id": "WUA_STAT_25K_015911",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=93.73, μ=47.9, σ=20.... | z = 2.269. | {
"id": "WUA_STAT_25K_015912",
"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=30.58, μ=87.37, σ=1.... | z = -33.804. | {
"id": "WUA_STAT_25K_015913",
"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=87.55, μ=14.22, σ=17... | z = 4.085. | {
"id": "WUA_STAT_25K_015914",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=1.92; Var[X]=1.690. | {
"id": "WUA_STAT_25K_015915",
"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 ≈ 0.440. | {
"id": "WUA_STAT_25K_015916",
"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=62.25, μ=2.93, σ=10.... | z = 5.698. | {
"id": "WUA_STAT_25K_015917",
"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=7... | 95% CI ≈ [68.44, 75.20]. | {
"id": "WUA_STAT_25K_015918",
"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=9... | 95% CI ≈ [89.09, 104.63]. | {
"id": "WUA_STAT_25K_015919",
"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]=8.32; Var[X]=3.994. | {
"id": "WUA_STAT_25K_015920",
"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 ≈ [129.76, 132.10]. | {
"id": "WUA_STAT_25K_015921",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=2.22; Var[X]=2.087. | {
"id": "WUA_STAT_25K_015922",
"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=58.31, μ=26.1, σ=4.4... | z = 7.255. | {
"id": "WUA_STAT_25K_015923",
"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]=28.86; Var[X]=7.504. | {
"id": "WUA_STAT_25K_015924",
"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": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.473. | {
"id": "WUA_STAT_25K_015925",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
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"license": "cc-by-4.0",
"tags": [... | [
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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=38.34, μ=34.42, σ=11... | z = 0.338. | {
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"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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [109.93, 123.09]. | {
"id": "WUA_STAT_25K_015927",
"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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}
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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]=8.12; Var[X]=5.846. | {
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"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",
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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=54.25, μ=93.86, σ=17... | z = -2.217. | {
"id": "WUA_STAT_25K_015929",
"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": "Compute z=(x-μ)/σ. Given x=97.66, μ=71.68, σ=24... | z = 1.046. | {
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"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": "Compute z=(x-μ)/σ. Given x=65.96, μ=18.95, σ=17... | z = 2.634. | {
"id": "WUA_STAT_25K_015931",
"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=5... | 95% CI ≈ [51.95, 56.21]. | {
"id": "WUA_STAT_25K_015932",
"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]=1.70; Var[X]=1.615. | {
"id": "WUA_STAT_25K_015933",
"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]=10.98; Var[X]=4.282. | {
"id": "WUA_STAT_25K_015934",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=3.91; Var[X]=3.011. | {
"id": "WUA_STAT_25K_015935",
"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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} |
{
"messages": [
{
"role": "system",
"content": "You 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 ≈ 0.883. | {
"id": "WUA_STAT_25K_015936",
"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]=3.04; Var[X]=2.554. | {
"id": "WUA_STAT_25K_015937",
"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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} |
{
"messages": [
{
"role": "system",
"content": "You 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 ≈ 0.424. | {
"id": "WUA_STAT_25K_015938",
"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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{
"messages": [
{
"role": "system",
"content": "You 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 ≈ 0.558. | {
"id": "WUA_STAT_25K_015939",
"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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{
"messages": [
{
"role": "system",
"content": "You 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 ≈ 0.711. | {
"id": "WUA_STAT_25K_015940",
"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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{
"messages": [
{
"role": "system",
"content": "You 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 ≈ 0.937. | {
"id": "WUA_STAT_25K_015941",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=14.80; Var[X]=9.324. | {
"id": "WUA_STAT_25K_015942",
"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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{
"messages": [
{
"role": "system",
"content": "You 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]=5.36; Var[X]=1.769. | {
"id": "WUA_STAT_25K_015943",
"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": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.096. | {
"id": "WUA_STAT_25K_015944",
"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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [133.15, 143.13]. | {
"id": "WUA_STAT_25K_015945",
"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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=7.98; Var[X]=4.948. | {
"id": "WUA_STAT_25K_015946",
"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=1... | 95% CI ≈ [155.24, 163.78]. | {
"id": "WUA_STAT_25K_015947",
"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.... | [
{
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"evidence_type": "self_contained",
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}
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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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [157.45, 158.17]. | {
"id": "WUA_STAT_25K_015948",
"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 ≈ 0.400. | {
"id": "WUA_STAT_25K_015949",
"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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [177.58, 186.74]. | {
"id": "WUA_STAT_25K_015950",
"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 ≈ [138.16, 161.90]. | {
"id": "WUA_STAT_25K_015951",
"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]=5.92; Var[X]=4.973. | {
"id": "WUA_STAT_25K_015952",
"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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} |
{
"messages": [
{
"role": "system",
"content": "You 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=43.74, μ=90.93, σ=22... | z = -2.116. | {
"id": "WUA_STAT_25K_015953",
"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]=17.68; Var[X]=8.486. | {
"id": "WUA_STAT_25K_015954",
"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,
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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=7... | 95% CI ≈ [75.37, 80.99]. | {
"id": "WUA_STAT_25K_015955",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=2.99; Var[X]=2.601. | {
"id": "WUA_STAT_25K_015956",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=22.57; Var[X]=8.802. | {
"id": "WUA_STAT_25K_015957",
"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=6... | 95% CI ≈ [61.42, 62.76]. | {
"id": "WUA_STAT_25K_015958",
"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=4... | 95% CI ≈ [34.97, 46.95]. | {
"id": "WUA_STAT_25K_015959",
"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 ≈ 0.729. | {
"id": "WUA_STAT_25K_015960",
"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 ≈ 0.340. | {
"id": "WUA_STAT_25K_015961",
"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 ≈ [56.99, 60.75]. | {
"id": "WUA_STAT_25K_015962",
"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 ≈ [140.85, 158.97]. | {
"id": "WUA_STAT_25K_015963",
"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]=18.90; Var[X]=6.993. | {
"id": "WUA_STAT_25K_015964",
"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 ≈ [119.46, 125.38]. | {
"id": "WUA_STAT_25K_015965",
"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=13.97, μ=1.06, σ=3.2... | z = 3.997. | {
"id": "WUA_STAT_25K_015966",
"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=52.57, μ=79.95, σ=15... | z = -1.768. | {
"id": "WUA_STAT_25K_015967",
"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=4... | 95% CI ≈ [38.91, 42.43]. | {
"id": "WUA_STAT_25K_015968",
"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 ≈ [146.09, 166.01]. | {
"id": "WUA_STAT_25K_015969",
"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 ≈ 0.564. | {
"id": "WUA_STAT_25K_015970",
"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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} |
{
"messages": [
{
"role": "system",
"content": "You 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]=1.56; Var[X]=1.466. | {
"id": "WUA_STAT_25K_015971",
"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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} |
{
"messages": [
{
"role": "system",
"content": "You 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=38.43, μ=39.09, σ=3.... | z = -0.203. | {
"id": "WUA_STAT_25K_015972",
"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]=0.70; Var[X]=0.665. | {
"id": "WUA_STAT_25K_015973",
"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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} |
{
"messages": [
{
"role": "system",
"content": "You 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 ≈ [44.97, 47.81]. | {
"id": "WUA_STAT_25K_015974",
"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 ≈ 0.851. | {
"id": "WUA_STAT_25K_015975",
"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=9... | 95% CI ≈ [98.15, 101.33]. | {
"id": "WUA_STAT_25K_015976",
"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=6... | 95% CI ≈ [54.82, 66.62]. | {
"id": "WUA_STAT_25K_015977",
"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]=3.96; Var[X]=3.089. | {
"id": "WUA_STAT_25K_015978",
"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]=11.40; Var[X]=7.980. | {
"id": "WUA_STAT_25K_015979",
"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 ≈ 0.051. | {
"id": "WUA_STAT_25K_015980",
"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 ≈ 0.519. | {
"id": "WUA_STAT_25K_015981",
"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=3... | 95% CI ≈ [32.19, 36.01]. | {
"id": "WUA_STAT_25K_015982",
"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 ≈ 0.266. | {
"id": "WUA_STAT_25K_015983",
"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=1... | 95% CI ≈ [124.70, 133.74]. | {
"id": "WUA_STAT_25K_015984",
"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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [151.27, 161.59]. | {
"id": "WUA_STAT_25K_015985",
"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=70.21, μ=31.88, σ=7.... | z = 5.159. | {
"id": "WUA_STAT_25K_015986",
"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=9... | 95% CI ≈ [90.14, 97.80]. | {
"id": "WUA_STAT_25K_015987",
"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=65.6, μ=31.38, σ=14.... | z = 2.441. | {
"id": "WUA_STAT_25K_015988",
"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=6... | 95% CI ≈ [48.36, 75.28]. | {
"id": "WUA_STAT_25K_015989",
"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=61.86, μ=86.88, σ=7.... | z = -3.386. | {
"id": "WUA_STAT_25K_015990",
"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": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [105.86, 121.62]. | {
"id": "WUA_STAT_25K_015991",
"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 ≈ [123.68, 127.08]. | {
"id": "WUA_STAT_25K_015992",
"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=61.14, μ=91.57, σ=10... | z = -2.946. | {
"id": "WUA_STAT_25K_015993",
"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": "Compute z=(x-μ)/σ. Given x=42.66, μ=95.09, σ=13... | z = -3.975. | {
"id": "WUA_STAT_25K_015994",
"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 ≈ 0.309. | {
"id": "WUA_STAT_25K_015995",
"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 ≈ 0.481. | {
"id": "WUA_STAT_25K_015996",
"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=76.83, μ=28.7, σ=9.9... | z = 4.847. | {
"id": "WUA_STAT_25K_015997",
"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 ≈ 0.674. | {
"id": "WUA_STAT_25K_015998",
"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=5... | 95% CI ≈ [48.85, 60.99]. | {
"id": "WUA_STAT_25K_015999",
"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 ≈ 0.327. | {
"id": "WUA_STAT_25K_016000",
"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"
} |
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