Discover, or rediscover, the special properties of the normal distribution

The assumption that a phenomenon follows a normal distribution is often used, at least as a first approximation. There are various statistical tests available to confirm (or refute) the normal a priori for the parent distribution of a sample (see section "Going further").

The properties of a normal distribution are well known, and tables (now Excel functions, for example) can be used to perform any desired probability calculation. In general, we remember and frequently use the following properties:

• 68.27% of values are within the range $\left[\mu -\sigma ;\mu +\sigma \right]$

• 95.45% of values are within the interval...