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The standard normal distribution is a normal distribution of standardized values called z-scores . A z-score is measured in units of the standard deviation. For example, if the mean of a normal distribution is 5 and the standard deviation is 2, the value 11 is 3 standarddeviations above (or to the right of) the mean. The calculation is:

x  =  μ  +  ( z ) σ  =  5  +  ( 3 ) ( 2 )  =  11

The z-score is 3.

The mean for the standard normal distribution is 0 and the standard deviation is 1. The transformation

z = x - μ σ produces the distribution Z ~ N ( 0 , 1 ) . The value x comes from a normal distribution with mean μ and standard deviation σ .

Practice Key Terms 2

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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