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 an applicant is randomly selected, find the probability of a rating that is between 200
And 275.

Question

Quizplus · Accepted Answer

The probability of a rating between 200 and 275 is found by calculating the area under the normal distribution curve between these two values. The Z-score for 275 is (275-200)/50 = 1.5. The probability of a Z-score less than 1.5 is 0.9332. Since the mean is 200, the probability of a rating less than 200 is 0.5. Therefore, the probability of a rating between 200 and 275 is 0.9332 - 0.5 = 0.4332.

A Bank's Loan Officer Rates Applicants for Credit