Example Suppose the grades of a large size class have a mean

Example: Suppose the grades of a large size class have a mean of 72 and a standard deviation of 9.

What is the probability that the average grade of a random sample of 36 students will be above 76?

The sample average ( ) has a normal distribution of mean

Solution

given mean =72

s.d = 9

76- mean =4

which is nearly half of standard deviation

for normal distribution we get through following

difference between the 76 and mean 4 and distance by 0.0

P(x >76) = 1 - P(x< 76) = 1- 0.5 - 0.19 = 0.31