In probability theory, a continuity correction is an adjustment that is made when a discrete distribution is approximated by a continuous distribution.
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 sizeis large enough. The binomial distribution can be approximated with a normal distribution too, as long as n*p and n*q are both greater than equal to 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 0.5 to the discrete x-value: use the following table to decide whether to add or subtract.
If
P(X=n) use P(n – 0.5 < X < n +
0.5)
If P(X>n) use P(X > n + 0.5)
If P(X?n) use P(X < n + 0.5)
If P (X<n) use P(X < n – 0.5)
If P(X ? n) use P(X > n – 0.5)
Example:
If P(X?351), use P (X?351-0.5)= P (X?350.5)
On the other hand, when the normal approximation is used to approximate a discrete distribution, a continuity correctioncan be employed so that we can approximate the probability of a specific value of the discrete distribution.
Describe the continuity correction (covered in an earlier course unit), and explain how, when, ...