Question

假設每天從甲地去乙地的旅客人數(shù)X是服從正態(tài)分布N(800,50²)的隨機變量，則一天中從甲地去乙地的旅客人數(shù)不超過900的概率P₀=（   ）
(參考數(shù)據(jù):若X～N(μ,σ²),有P(μ-σ<X≤μ+σ)=0.6826,P(μ-2σ<X≤μ+2σ)=0.9544,
P(μ-3σ<X≤μ+3σ)=0.9974．)

A．0.954

B．0.9974

C．0.9772

D．0.9773

Answer 1

C

由于隨機變量X服從正態(tài)分布N(800,50²),故有μ=800,σ=50,P(700<X≤900)=0.9544．由正態(tài)分布的對稱性,可得
P₀=P(X≤900)=P(X≤800)+P(800<X≤900)=+P(700<X≤900)=0.9772