Find the indicated probability or percentage for the normally distributed variable.
-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.
A)0.4332
B)0.9332
C)0.0668
D)0.5

Question

Find the indicated probability or percentage for the normally distributed variable.
-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. 
A)0.4332
B)0.9332
C)0.0668
D)0.5

Quizplus · Accepted Answer

The probability of a rating between 200 and 275 can be found using the standard normal distribution. First, calculate the z-scores for 200 and 275. The z-score for 200 is 0, and for 275 is (275-200)/50 = 1.5. Using the standard normal distribution table, the probability for z = 1.5 is approximately 0.9332, and for z = 0 is 0.5. The probability of being between these two z-scores is 0.9332 - 0.5 = 0.4332.

Find the Indicated Probability or Percentage for the Normally Distributed