The normal distribution is often used as a model in practical situations. When a problem is set in a practical context the first task is to convert the information into the language of the normal distribution. If the variable X is normally distributed with mean \mu and standard deviation \sigma then

\qquad \qquad P(X \le x) = \displaystyle \Phi \left(\frac{x-\mu}{\sigma}\right)

\qquad \qquad P(X \le x) = \displaystyle \Phi \left(\frac{x-\mu}{\sigma}\right)

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## Glossary

### mean

the sum of all the members of the list divided by the number of items in the list.

### normal distribution

A key distribution in statistics which is used to model many naturally occurring phenomena, such as heights and weights; its distribution is bell-shaped.

### standard deviation

The square root of the variance; a measure of dispersion.

### union

The union of two sets A and B is the set containing all the elements of A and B.

### variable

A value which is unknown and free to vary, often denoted by x or y.