where \hat p = n_S / n is the proportion of successes in a Bernoulli trial process with n trials yielding n_S successes and n_F = n - n_S failures, and z is the 1 - \tfrac{1}{2}\alpha quantile of a standard normal distribution corresponding to the target error rate \alpha.
The central limit theorem applies poorly to this distribution with a sample size less than 30 or where the proportion is close to 0 or 1.