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. 0.5000 c. 0.4332 d. 1.0668

Explanation:

Step1: Calculate the z - scores

The formula for the z - score 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 $x = 200$, $z_1=\frac{200 - 200}{50}=0$
For $x = 275$, $z_2=\frac{275 - 200}{50}=\frac{75}{50}=1.5$

Step2: Use the standard normal distribution table

We want to find $P(0Then $P(0

Answer:

C. 0.4332