This formula can be rearranged as follows to reveal departures from the normal approximation:

Wilson and colleagues determined that the Schipper values were close approximations to the normal approximation to the binomial distribution.

Using a normal approximation the target standard error is approximately .05.

How close is this to what a normal approximation would give?

A hypothesis test using normal approximation for discrete data.

Because FPR is so small, we do not use a normal approximation.

In probability theory, the de Moivre-Laplace theorem is a normal approximation to the binomial distribution.

The normal approximation fails totally when the sample proportion is exactly zero or exactly one.

In statistics, McNemar's test is a normal approximation used on nominal data.

The addition of 0.5 is the continuity correction; the uncorrected normal approximation gives considerably less accurate results.