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Anaheim Human Resources, Inc., performs employment screenings 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 between a certain range, they are called in for a 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 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:
76 75 74 56 61 76
62 96 68 62 78 76
84 67 60 96 77 59
67 81 66 71 69 65
58 77 82 75 76 67
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. Based on the data the assumption of a bell-shaped distribution, what score should be used for the two cutoffs?
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