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

adOrmaPem6r 2021-11-10 Answered
Suppose that X is a normal random variable with mean 5. If P{X>9}=.2, approximately what is Var(X)?
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Ched1950
Answered 2021-11-11 Author has 21 answers

Given: X is a normal random variable with mean μ=5 and P[X>9]=0.2
To find: variance of X
Solution: Let σ2 be the variance of X. Now,
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
Thus variance of X is var(X)=σ2=(4.73)2=22.37=22

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