Suppose that X is a normal random variable with mean 5. If P{X>9}=.2, approximat

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Answered question

2021-11-10

Suppose that X is a normal random variable with mean 5. If P{X>9}=.2, approximately what is Var(X)?

Answer & Explanation

Ched1950

Ched1950

Beginner2021-11-11Added 21 answers

X is an averaged, normal random variable. 

μ=5 and P[X>9]=0.2
Let X's variance be σ2 then.,
P[X>9]=0.2
P[X9]=10.2=0.8
P[xμσ94σ]=0.8
P[Z4σ]=0.8
ϕ(4σ)=0.8
4σ=0.845
σ=40.845=4.73
Therefore, X's variance is

var(X)=σ2=(4.73)2=22.37=22

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