You are given a population mean of 75, population standard deviation of 5 and a sample size of 40. Solve for the standard error wherein the standard error = population standard deviation divided by the square root of sample size.
Error = 5/√40 = 0.791
If score is less than 74, then
z-score = actual score minus the population score divided by standard error.
z-score = 74-75/0.791 = -1.26
Find this value in the area under the distribution curve to the left of the z score of -1.26 and you will find that it is 0.1038. It means that the probability of getting a z-score of less than or equal to -1.26 is equal to 10.38%.
