A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If 40 different applicants are randomly selected, find the probability that their mean is above 215.

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean will have a mean of 200 and a standard deviation of 50/sqrt(40). To find the probability that the sample mean is above 215, calculate the z-score: (215-200)/(50/sqrt(40)) = 1.897. Using the standard normal distribution table, the probability of a z-score above 1.897 is approximately 0.0287.

A Bank's Loan Officer Rates Applicants for Credit