z- Score

z- Score

If a normal distribution has mean µ and standard deviation \sigma, then the z-score for the number x is

z = \frac{x-\mu }{\sigma }.

 

Example:- If a normal distribution has mean 50 and standard deviation 4, find the following

z-scores. The z-score for x= 46

 

Solution :- Since 46 is 4 units below 50 and the standard deviation is 4, 46 is

1 standard deviation below the mean. So, its z-score is -1.

 

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