The normal distribution is often used as an approximation to the distribution of values in a discrete population. In such situations, extra care should be taken to ensure that probabilities are computed in an accurate manner.
The correction for discreteness of the underlying distribution in Example 4.19 -that is, the addition or subtraction of .5 before standardizing- is often called a continuity correction. It is useful in the following application of the normal distribution to the computation of binomial probabilities.