A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and astandard deviation of 50. If 70 different applicants are randomly selected, find the likelihood that their mean is above 215.

Question

Quizplus · Accepted Answer

The standard error of the mean is 50/sqrt(70). The z-score for a sample mean of 215 is (215-200)/(50/sqrt(70)). Using the z-table, the probability of the mean being above 215 corresponds to a z-score of approximately 2.33, which is about 0.0062.

A Bank's Loan Officer Rates Applicants for Credit