A bank's loan officer rates applicants for credit.The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50.If an applicant is randomly selected,what percentage can be expected to be between 200 and 275?
A)6.68%
B)43.32%
C)93.32%
D)42.37%
E)5.00%

Question

Quizplus · Accepted Answer

Since the ratings follow a normal distribution with mean 200 and standard deviation 50, we can standardize the scores using the formula z = (x - μ)/σ. Then, to find the percentage of applicants between 200 and 275, we compute:

z1 = (200 - 200)/50 = 0
z2 = (275 - 200)/50 = 1.5

Using a standard normal distribution table or calculator, we can find the proportion of values between z1 and z2, which is approximately 0.4332 or 43.32%. Therefore, the answer is B.

A Bank's Loan Officer Rates Applicants for Credit