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 range
to
is
if
is small.
The Normal distribution is written
where
is the mean and
is the standard deviation. It has three characteristics:
-
It is symmetric about the mean
\[\mu\]. -
Virtually all occurrences occur within three standard deviations of the mean.
-
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.