Question: A bank's loan office rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50.

a) If one applicant is randomly selected, find the probability that the rating is between 200-235.

b) If one applicant is randomly selected, find the probability that the rating is above 250.

c) If one applicant is randomly selected, find the probability that the rating is between 210-260.

d) Find D₆, the rating which separates the lower 60% from the top 40%.

e) If 30 different applicants are randomly selected, find the probability that their mean rating is below \(220\).