When we approximate a discrete distribution, such as the binomial, by a continuous distribution, such as the normal, we need to make adjustments so “things don’t fall in the cracks.”

From the Central Limit Theorem, we know that a sample distribution from a population, even a non-normal one, becomes normal if the sample size is large enough. Though we often think of “large enough” to be 30, we need to be careful with binomial distributions.

For binomial distributions, which are defined by n and the proportion/probability p, both n times p and n times q, which is (1-p), need to be greater than 5. Once we confirm that both are greater than 5, we need to apply the continuity correction before we are able to use the normal curve to find our answers.

Remember that a binomial distribution is a discrete distribution and can only take integers as values. The normal distribution can take any real number, which means fractions or decimals. Thus, the binomial has “cracks” while the normal does not.Continuity Correction – Filling the cracks in the Normal Approximation to the Binomial