Lake Wobegon Junior College admits students only if they score above 1200 on the sum of their critical reading, mathematics, and writing scores. Applicants from ethnic group A have a mean of 1500 and a standard deviation of 300 on this test, and applicants from ethnic group B have a mean of 1350 and a standard deviation of 200. Both distributions are approximately normal.
a. Find the proportion not admitted for each ethnic group.
b. Both ethnic groups have the same size. Of the students who are not admitted, what proportion is from group B?
c. A state legislator proposes that the college lower the cutoff point for admission to 600, thinking that of the students who are not admitted, the proportion from ethnic group B would decrease. If this policy is implemented, determine the effect on the answer to part b, and comment.