已知随机变量X服从正态分布N(μ,σ2),且P(μ-2σ<X≤μ+2σ)=0.9544,P(μ-σ<X≤μ+σ)=0.682

2025-01-21 12:23:51
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回答1:

∵随机变量X服从正态分布N(μ,σ2),P(μ-2σ<X≤μ+2σ)=0.9544,P(μ-σ<X≤μ+σ)=0.6826,μ=4,σ=1,
∴P(2<X≤6)=0.9544,P(3<X≤5)=0.6826,
∴P(2<X≤6-P(3<X≤5)=0.9544-0.6826=0.2718,
∴P(5<X<6)=

1
2
×0.2718=0.1359
故答案为:0.1359