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 170 and 220.
A)0.2257
B)0.1554
C)0.0703
D)0.3811

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 170 and 220. 
A)0.2257
B)0.1554
C)0.0703
D)0.3811

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 value, μ is the mean, and σ is the standard deviation. For X=170, Z = (170 - 200) / 50 = -0.6. For X=220, Z = (220 - 200) / 50 = 0.4. Looking these Z-scores up in a standard normal distribution table or using a calculator, the probability between Z = -0.6 and Z = 0.4 is approximately 0.3811.

Find the Indicated Probability or Percentage for the Normally Distributed