3 years ago
Suppose that X is a normal random variable with mean 5. If P(X>9)=.2, ~imately what is Var(X)?
1 Answers
Best Answer
mmmmmm Staff answered 3 years ago
mmmmmm Staff answered 3 years ago
Given: X is a normal random variable with mean mu=5 and P[X>9]=0.2
To find: variance of X
Solution: Let sigma^2 be the variance of X. Now,
P[X>9]=0.2
-> P[X <=9]=1-0.2=0.8
-> P[ (x- mu)/(sigma) <= (9-4)/(sigma)]=0.8
-> P[Z <= (4)/(sigma)]=0.8
-> phi ((4)/(sigma))=0.8
-> (4)/(sigma)=0.845
-> sigma= (4)/(0.845)=4.73
Thus variance of X is var(X)= sigma^2=(4.73)^2=22.37=22