## Normal Approximation

Suppose that is a binomial random variable with and . If the size is adequately large, then the distribution of can be approximated by the normal distribution with mean = and standard deviation = . That is, a normal distribution approximates a binomial distribution. A general rule for ``adequately large'' is to satisfy and .

Let be a normal random variable whose distribution approximates the binomial distribution of a random variable . Then the probability involving can be approximated by that of . Having taken into account the fact that is a continuous random variable, the approximated probability

=
.

is calculated with continuity correction.