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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:
The z-score is 3.
The mean for the standard normal distribution is 0 and the standard deviation is 1. The transformation
$z=\frac{x-\mu}{\sigma}\phantom{\rule{10pt}{0ex}}$ produces the distribution $Z$ ~ $N(0,1)\phantom{\rule{15pt}{0ex}}$ . The value $x$ comes from a normal distribution with mean $\mu $ and standard deviation $\sigma $ .
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