



 
Hi Barb, In probability and statistics the letter Z is used for the random variable which has the standard normal distribution, that is the normal distribution with mean 0 and standard deviation 1. Many times we have a random variable X from the normal distribution with some mean μ and standard deviation σ, and we convert it to the standard normal random variable Z using the so called Zscore. Lets look at a specific example. Suppose you have a normal distribution with mean μ = 5 and standard deviation σ = 3. If the random variable that satisfies this distribution is X then Suppose you now take a measurement from this distribution and obtain a value X = 11. This gives Z = 2 or said using symbols Multiplying both sides by σ gives
which says that 11 is 2 standard deviations more than the mean. Suppose we take another measurement X and this time get Z = 1.5. Then
and hence X is one and a half standard deviations less than the mean. Hence the Zscore tell us how far X is from the mean using the units of standard deviation. I hope this helps,  


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