6.1 The standard normal distribution

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

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