4.54. Lake Wobegon Junior College admits students only if they score above 400 on a standardized achievement test. Applicants from group A have a mean of 500 and a standard deviation of 100 on this test, and applicants from group B have a mean of 450 and a standard deviation of 100. Both distributions are approximately normal, and both groups have the same size.

(a) Find the proportion not admitted for each group.

(b) Of the students who arc not admitted, what proportion are from group B?

(c) A state legislator proposes that the college lower the cutoff point for admission to 300, thinking that the proportion of the students who are not admitted who are from group B would decrease. If this policy is implemented, determine the effect on the answer to (b), and comment.