A bank loan officer rates applicants for credit. The ratings are normally disterbuted with a mean of 600 and a standard deviation of 200.

Define first.

Let X represent the rating of applicant.

Then, X \sim N(600, 200^2)

Then, P(600 < X < 775) = P\(\frac{600 - \mu}{\sigma} < z < \frac{775 - \mu}{\sigma}\)

Replace the values, and find this probability.

What do you get? :)