Abank'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. your answer should be a decimal rounded to the fourth decimal place.

The probability is 0.1915.

We find the z-scores associated with this interval using the formula

z = (X-μ)/σ

For the lower limit, we have
z = (200-200)/50=0

Using a z-table (http://www.z-table.com) we see that the area under the curve to the left of, less than, this is 0.5000.

For the upper limit, we have
z = (275-200)/50 = 0.5

Using a z-table (http://www.z-table.com) we see that the area under the curve to the left of, less than, this is 0.6915.

To find the area between these two ends, we subtract:
0.6915 - 0.5000 = 0.1915.

Hope this ; )