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.