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. Using the Z-table, the probability of Z being less than 1.5 is approximately 0.9332. Since the probability of a score being less than the mean (200) is 0.5 (due to the symmetry of the normal distribution), the probability of a score between 200 and 275 is 0.9332 - 0.5 = 0.4332.

A Bank's Loan Officer Rates Applicants for Credit