Question

a banks 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. round to four decimal places.

a. 0.9332
b. 0.4332
c. 0.0668
d. 0.5000

Explanation:

Step1: Calculate the z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set. For $\mu = 200$, $\sigma=50$, when $x = 200$, $z_1=\frac{200 - 200}{50}=0$. When $x = 275$, $z_2=\frac{275 - 200}{50}=\frac{75}{50}=1.5$.

Step2: Use the standard normal distribution table

We want to find $P(0

Answer:

B. 0.4332