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

To find the probability of a rating between 200 and 275, we use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For X=275, Z = (275-200)/50 = 1.5. Looking up 1.5 in the Z-table gives us the probability of 0.9332. However, since we're looking for the probability between the mean (200) and 275, we subtract the probability of being below the mean (0.5) from 0.9332, resulting in 0.4332.

A Bank's Loan Officer Rates Applicants for Credit