[{"data":1,"prerenderedAt":190},["ShallowReactive",2],{"topic-page:\u002Fhigh-school\u002Fmathematics-b\u002Fprobability-distributions\u002Fnormal-approximation-to-binomial":3},{"topic":4,"category":154,"seo":159,"breadcrumbs":164,"prerequisites":171,"nextTopics":180,"relatedTopics":189},{"id":5,"slug":6,"title":7,"summary":8,"canonicalPath":9,"categoryPath":10,"difficulty":11,"targetAudience":12,"estimatedMinutes":13,"generatedAt":14,"publishedAt":14,"updatedAt":14,"reviewStatus":15,"tags":16,"expectedKnowledge":21,"learningGoal":24,"blocks":25},"high-school-mathematics-b-probability-distributions-normal-approximation-to-binomial","normal-approximation-to-binomial","二項分布の正規近似","試行回数が十分大きい二項分布を同じ平均・分散の正規分布で近似し、連続補正で整数の境界を面積へ移します。","\u002Fhigh-school\u002Fmathematics-b\u002Fprobability-distributions\u002Fnormal-approximation-to-binomial","\u002Fhigh-school\u002Fmathematics-b\u002Fprobability-distributions","beginner","student_high",6,"2026-07-27","ai_generated",[17,18,19,20],"数学B","統計的な推測","正規近似","連続補正",[22,23],"二項分布の平均と分散","正規分布の標準化","二項分布の正規近似が使える場面を判断し、連続補正を施して対応する正規分布の区間確率へ変換できる。",[26,31,41,71,77,87,107,113,119,135,144],{"id":27,"type":28,"title":7,"subtitle":29,"shortDefinition":30},"hero","HeroBlock","整数の棒を連続な釣鐘形の面積へ置き換える","試行回数が十分大きい二項分布は、同じ平均と分散をもつ正規分布で近似できます。整数ごとの棒を面積へ移すときは、境界を0.5ずらす連続補正を使います。",{"id":32,"type":33,"term":34,"definition":35,"plainExplanation":36,"keywords":37},"definition","DefinitionBlock","正規近似と連続補正","離散的な二項分布を連続な正規分布で近似し、整数の範囲を半整数の境界へ直すことです。","二項分布の棒が滑らかな釣鐘形へ近づくと、たくさんの二項確率の和を正規曲線の面積で見積もれます。ただしX=54の棒にも横幅があると考え、X≤54は連続変数Y≤54.5へ対応させます。この0.5の調整が連続補正です。",[38,39,40],"同じ平均と分散","半整数の境界","近似",{"id":42,"type":43,"title":44,"lead":45,"formulas":46,"strategy":70},"formula","FormulaBlock","近似する正規分布","XがB(n,p)に従い、q=1−pとします。",[47,61],{"label":19,"expression":48,"meaning":49,"symbols":50,"tip":60},"X≈Y, 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