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

To find the probability of a rating between 170 and 220, we use the Z-score formula: Z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. For X=170, Z1 = (170 - 200) / 50 = -0.6. For X=220, Z2 = (220 - 200) / 50 = 0.4. Looking these Z-scores up in a standard normal distribution table or using a calculator, the probability between Z1 and Z2 is approximately 0.3811.

A Bank's Loan Officer Rates Applicants for Credit