Show that if  X is a discrete random variable a mean of  mu and a standard deviation sigma, then  Z=(X-mu)/sigma is a discrete random variable with a mean of zero and a standard deviation of 1

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Show that if  X is a discrete random variable a mean of  mu and a standard deviation sigma, then 

Z=(X-mu)/sigma is a discrete random variable with a mean of zero and a standard deviation of 1

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In SD(X-mu/sigma)=1/sigma * SD(X)

What happened to the mean mu? 

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