Describe the idea of continuity correction and explain why i

Describe the idea of \"continuity correction\" and explain why it is necessary in approximating a binomial distribution probability?

Solution

A continuity correction factor is used when you use a continuous function to approximate a discrete one. For example, when you want to approximate a binomial with a normal distribution. According to the Central Limit Theorem, the sample mean of a distribution becomes approximately normal if the sample size is large enough. The binomial distribution can be approximated with a normal distribution too, as long as n*p and n*q are both at least 5.

The continuity correction factor a way to account for the fact that a normal distribution is continuous, and a binomial is not. When you use a normal distribution to approximate a binomial distribution, you’re going to have to use a continuity correction factor. It’s as simple as adding or subtracting .5 to the discrete x-value: use the following table to decide whether to add or subtract.