Please help explain the question

Question

If X is a normal random variable with mean and standard deviation, write P (a< X < b) in terms of the probabilities associated with the standard normal random variable Z.

Answer 1

You want to translate everything into standard normal.  Subtract the mean from a,X, and b and divide by the standard deviation.

 

P(((a-μ)/σ)<Z<((b-μ)/σ))