Question: Anaheim Human Resources, Inc., performs employment screening for large companies in southern California. It usually follows a two-step process. First, potential applicants are given a test that covers basic knowledge and intelligence. If applicants score within a certain range, they are called in for an interview. If they score below a certain point, they are sent a rejection letter. If applicants score above a certain point, they are sent directly to the client's human resources office without the interview. Recently, Anaheim Human Resources began working with a new client and formulated a new test just for this company. Thirty people were given the test, which is supposed to produce scores that are distributed according to a bell-shaped distribution. The following data reflect the scores of those 30 people:
Anaheim Human Resources has in the past issued a rejection letter with no interview to the lower 16% taking the test. They also send the upper 2.5% directly to the company without an interview. Everyone else is interviewed. Based on the data and the assumption of a bell-shaped distribution, what score should be used for the two cutoffs?