Suppose X∼Normal(μ,σ).
Define a new random variable Z by Z=X−μσ.
Fact: Z also follows a Normal distribution. What are the mean (i.e., expected value) and variance of Z?
"Recall" that if X is a random variable and a is a number, then
E(aX)=aE(X)
E(X+a)=E(X)+a
SD(aX)=a2SD(X)