## Introducing the Normal Distribution

The normal distribution is the most useful, adaptable, flexible, used statistical distribution there is. All other distributions are, in a sense, subsumed by it because of the Central Limit Theorem, which says that in some circumstances any statistical distribution can be modelled by a normal distribution.

The probability of any occurrence in the rangetoisifis small.

The Normal distribution is writtenwhereis the mean andis the standard deviation. It has three characteristics:

1. It is symmetric about the mean

$\mu$
.

2. Virtually all occurrences occur within three standard deviations of the mean.

3. The normal distribution is bell shaped.

There are some limitations for the normal which means it cannot be a possible exact distribution for certain quantities, even though it may be a good approximation. For example, the normal allows negative occurrences, but negative lengths are not possible, so it cannot be a possible distribution for lengths of worms.

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