The Continuity Correction

The normal distribution is a continuous distribution,but it can in fact also be used to model the distribution of adiscrete random variable that fits the normal distribution. We dothis by introducing the continuity correction.

If we want to find the probability that a randomvariable takes the value k then we find

If we want to find the probability that a randomvariable takes any value less than or equal to k then we find

If we want to find the probability that a randomvariable takes any value less than k then we find

Notice the difference in the above two expressions. Because X maybe equal to k in the first of these two expressions,we haveinsteadof

If we want to find the probability that a randomvariable takes any value greater than or equal to k then we find

If we want to find the probability that a random variable takesany value greater than k then we find

Notice the difference in the above two expressions. Becausemaybe equal tointhe first of these two expressions,we haveinsteadof

Example: The number of worms perofsoil is normally distributed with mean 51.4 and variance 20. Find theprobability that the number of worms inis60.

To findso

To findso