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 170 and 220.

Question

Quizplus · Accepted Answer

The Z-scores for 170 and 220 are calculated as (170-200)/50 = -0.6 and (220-200)/50 = 0.4, respectively. Using the standard normal distribution table, the probability for Z = -0.6 is approximately 0.2743 and for Z = 0.4 is approximately 0.6554. The probability of a rating between 170 and 220 is 0.6554 - 0.2743 = 0.3811.

A Bank's Loan Officer Rates Applicants for Credit