Use of the normal approximation to the binomial distribution

To avoid adding large numbers of binomial probabilities, the normal approximation can be used to find the probability that a binomial variable is within a certain range when the sample size, n , is large.

A common rule-of-thumb for when this kind of normal approximation can be used is:

nπ > 5    and     n(1-π) > 5

An example is given below:

Note the translation of the range of values into one involving 1/2. It is called a continuity correction in this context.