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 have
insteadof
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. Because
maybe equal to
inthe first of these two expressions,we haveinsteadof
Example: The number of worms per
ofsoil is normally distributed with mean 51.4 and variance 20. Find theprobability that the number of worms in
is60.
To find
so
To find
so
