Normal Distribution: Standard Normal Distribution

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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 standard deviations above (or to the right of) the mean. The calculation is:

$x=\mu +(z)\sigma =5+\left ( 3 \right )\left ( 2 \right )=11$

The z-score is 3.

The mean for the standard normal distribution is 0 and the standard deviation is 1. The transformation $z=\frac{x-\mu }{\sigma }$ produces the distribution Z∼ N (0, 1) . The value x comes from a normal distribution with mean µ and standard deviation σ.

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Normal Distribution: Standard Normal Distribution