prompt dict | response string | meta dict | fact_sources list | artifacts dict |
|---|---|---|---|---|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=9.72; Var[X]=4.471. | {
"id": "WUA_STAT_25K_011001",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.304. | {
"id": "WUA_STAT_25K_011002",
"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=58.81, μ=7.81, σ=13.... | z = 3.682. | {
"id": "WUA_STAT_25K_011003",
"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 ≈ 0.501. | {
"id": "WUA_STAT_25K_011004",
"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=8... | 95% CI ≈ [76.70, 84.50]. | {
"id": "WUA_STAT_25K_011005",
"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=18.3, μ=89.81, σ=15.... | z = -4.526. | {
"id": "WUA_STAT_25K_011006",
"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]=8.96; Var[X]=3.942. | {
"id": "WUA_STAT_25K_011007",
"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]=15.66; Var[X]=6.577. | {
"id": "WUA_STAT_25K_011008",
"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]=9.80; Var[X]=4.998. | {
"id": "WUA_STAT_25K_011009",
"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]=17.25; Var[X]=4.312. | {
"id": "WUA_STAT_25K_011010",
"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 ≈ 0.955. | {
"id": "WUA_STAT_25K_011011",
"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 ≈ 0.810. | {
"id": "WUA_STAT_25K_011012",
"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]=7.80; Var[X]=4.758. | {
"id": "WUA_STAT_25K_011013",
"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=6... | 95% CI ≈ [66.23, 69.53]. | {
"id": "WUA_STAT_25K_011014",
"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 ≈ 0.353. | {
"id": "WUA_STAT_25K_011015",
"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=8... | 95% CI ≈ [78.36, 87.16]. | {
"id": "WUA_STAT_25K_011016",
"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]=12.22; Var[X]=6.477. | {
"id": "WUA_STAT_25K_011017",
"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 ≈ 0.903. | {
"id": "WUA_STAT_25K_011018",
"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 ≈ 0.451. | {
"id": "WUA_STAT_25K_011019",
"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 ≈ [13.95, 14.83]. | {
"id": "WUA_STAT_25K_011020",
"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 ≈ 0.432. | {
"id": "WUA_STAT_25K_011021",
"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=91.53, μ=77.63, σ=10... | z = 1.325. | {
"id": "WUA_STAT_25K_011022",
"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 ≈ 0.627. | {
"id": "WUA_STAT_25K_011023",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=7.65; Var[X]=3.748. | {
"id": "WUA_STAT_25K_011024",
"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": [
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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=9... | 95% CI ≈ [93.86, 102.06]. | {
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"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
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"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.... | [
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"messages": [
{
"role": "system",
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},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=2.79; Var[X]=1.925. | {
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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... | [
{
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"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
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"messages": [
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"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.209. | {
"id": "WUA_STAT_25K_011027",
"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": [... | [
{
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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": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.485. | {
"id": "WUA_STAT_25K_011028",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "archon",
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"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
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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 ≈ [5.49, 29.73]. | {
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"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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"role": "system",
"content": "You 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=80.94, μ=5.94, σ=5.1... | z = 14.451. | {
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"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "core",
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"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
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"source_url": "",
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"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 ≈ 0.219. | {
"id": "WUA_STAT_25K_011031",
"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 ≈ 0.651. | {
"id": "WUA_STAT_25K_011032",
"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]=16.79; Var[X]=4.533. | {
"id": "WUA_STAT_25K_011033",
"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 ≈ 0.734. | {
"id": "WUA_STAT_25K_011034",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [192.67, 205.13]. | {
"id": "WUA_STAT_25K_011035",
"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=6... | 95% CI ≈ [55.25, 64.93]. | {
"id": "WUA_STAT_25K_011036",
"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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"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 ≈ 0.305. | {
"id": "WUA_STAT_25K_011037",
"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=4... | 95% CI ≈ [45.32, 46.46]. | {
"id": "WUA_STAT_25K_011038",
"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]=10.92; Var[X]=6.334. | {
"id": "WUA_STAT_25K_011039",
"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=5... | 95% CI ≈ [43.91, 65.45]. | {
"id": "WUA_STAT_25K_011040",
"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]=9.88; Var[X]=7.311. | {
"id": "WUA_STAT_25K_011041",
"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]=8.28; Var[X]=2.567. | {
"id": "WUA_STAT_25K_011042",
"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 ≈ 0.585. | {
"id": "WUA_STAT_25K_011043",
"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 ≈ 0.526. | {
"id": "WUA_STAT_25K_011044",
"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
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} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.656. | {
"id": "WUA_STAT_25K_011045",
"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=85.31, μ=99.92, σ=6.... | z = -2.161. | {
"id": "WUA_STAT_25K_011046",
"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]=5.44; Var[X]=3.699. | {
"id": "WUA_STAT_25K_011047",
"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": "Compute z=(x-μ)/σ. Given x=24.04, μ=49.03, σ=7.... | z = -3.405. | {
"id": "WUA_STAT_25K_011048",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [174.01, 180.27]. | {
"id": "WUA_STAT_25K_011049",
"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 ≈ 0.657. | {
"id": "WUA_STAT_25K_011050",
"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=72.6, μ=46.0, σ=21.4... | z = 1.243. | {
"id": "WUA_STAT_25K_011051",
"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=79.73, μ=76.14, σ=12... | z = 0.289. | {
"id": "WUA_STAT_25K_011052",
"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 ≈ 0.125. | {
"id": "WUA_STAT_25K_011053",
"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]=17.70; Var[X]=7.257. | {
"id": "WUA_STAT_25K_011054",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=49.81, μ=90.78, σ=10... | z = -3.833. | {
"id": "WUA_STAT_25K_011055",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [173.60, 183.86]. | {
"id": "WUA_STAT_25K_011056",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=4.56; Var[X]=3.694. | {
"id": "WUA_STAT_25K_011057",
"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]=15.75; Var[X]=3.938. | {
"id": "WUA_STAT_25K_011058",
"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=45.53, μ=38.52, σ=14... | z = 0.491. | {
"id": "WUA_STAT_25K_011059",
"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 ≈ 0.586. | {
"id": "WUA_STAT_25K_011060",
"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 ≈ 0.537. | {
"id": "WUA_STAT_25K_011061",
"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 ≈ [136.55, 150.77]. | {
"id": "WUA_STAT_25K_011062",
"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 ≈ [5.24, 18.96]. | {
"id": "WUA_STAT_25K_011063",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=57.35, μ=82.94, σ=6.... | z = -4.088. | {
"id": "WUA_STAT_25K_011064",
"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=73.87, μ=75.94, σ=11... | z = -0.175. | {
"id": "WUA_STAT_25K_011065",
"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]=21.70; Var[X]=8.246. | {
"id": "WUA_STAT_25K_011066",
"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=8.25, μ=3.84, σ=11.6... | z = 0.380. | {
"id": "WUA_STAT_25K_011067",
"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]=8.32; Var[X]=2.995. | {
"id": "WUA_STAT_25K_011068",
"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=3.89, μ=67.12, σ=3.3... | z = -18.875. | {
"id": "WUA_STAT_25K_011069",
"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 ≈ 0.369. | {
"id": "WUA_STAT_25K_011070",
"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 ≈ 0.379. | {
"id": "WUA_STAT_25K_011071",
"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",
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},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=8... | 95% CI ≈ [77.88, 86.12]. | {
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"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=5.40; Var[X]=3.780. | {
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"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=2.90; Var[X]=1.218. | {
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},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [102.96, 116.42]. | {
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},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [193.74, 203.04]. | {
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"subdomain": "stats_math::confidence_intervals",
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"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.509. | {
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"task": "quantitative_reasoning",
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},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.699. | {
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"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
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},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.789. | {
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"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
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"license": "cc-by-4.0",
"tags": [
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},
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"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.276. | {
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"task": "quantitative_reasoning",
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},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=6.20; Var[X]=2.356. | {
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"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
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"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [117.57, 139.91]. | {
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"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
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"license": "cc-by-4.0"... | [
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"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=1... | 95% CI ≈ [17.83, 21.61]. | {
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"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
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"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0"... | [
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},
{
"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=13.75; Var[X]=6.188. | {
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"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained_math",
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"license": "cc-by-4.0",
"ta... | [
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{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.867. | {
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"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
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"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
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{
"role": "user",
"content": "Compute z=(x-μ)/σ. Given x=78.72, μ=72.94, σ=1.... | z = 5.255. | {
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"license": "cc-by-4.0",
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},
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"role": "user",
"content": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=1.10; Var[X]=0.990. | {
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"domain": "master_scholars_academics",
"subdomain": "stats_math::distributions",
"task": "quantitative_reasoning",
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"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"ta... | [
{
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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 ≈ [146.15, 154.31]. | {
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"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
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"license": "cc-by-4.0"... | [
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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": "For X~Binomial(n,p), E[X]=np and Var[X]=np(1-p)... | E[X]=1.19; Var[X]=0.988. | {
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"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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"content": "You 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 ≈ 0.045. | {
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"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
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"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]=8.06; Var[X]=5.561. | {
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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... | [
{
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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": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.169. | {
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"domain": "master_scholars_academics",
"subdomain": "stats_math::bayes",
"task": "quantitative_reasoning",
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"tags": [
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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 ≈ [141.57, 150.91]. | {
"id": "WUA_STAT_25K_011095",
"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 ≈ [103.29, 111.17]. | {
"id": "WUA_STAT_25K_011096",
"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 ≈ [2.74, 18.10]. | {
"id": "WUA_STAT_25K_011097",
"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=18.76, μ=24.36, σ=10... | z = -0.518. | {
"id": "WUA_STAT_25K_011098",
"domain": "master_scholars_academics",
"subdomain": "stats_math::standardization",
"task": "quantitative_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "95% CI (z-approx): x̄ ± 1.96*(s/√n). Given x̄=3... | 95% CI ≈ [31.48, 34.14]. | {
"id": "WUA_STAT_25K_011099",
"domain": "master_scholars_academics",
"subdomain": "stats_math::confidence_intervals",
"task": "quantitative_reasoning",
"difficulty": "core",
"truth_mode": "self_contained_math",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units."
},
{
"role": "user",
"content": "PPV=(sens·prev)/((sens·prev)+(1-spec)(1-prev)).... | PPV ≈ 0.525. | {
"id": "WUA_STAT_25K_011100",
"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"
} |
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