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To calculate probability value using normal distribution.
Robinson & Associates performs employment screening for large companies in southern California. It usually follows two-step process. First potential applicants are given a test that covers basic knowledge and intelligence. If applicants score between a certain ranges, 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, Robinson & Associates 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.
DATA
76
75
74
56
61
62
96
68
78
84
67
60
77
59
81
66
71
69
65
58
82
Robinson & Associates 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 percent directly to the company without an interview. Everyone else is interviewed. Based on the data and assumption of a bell-shaped distribution, what score should be used for the two cut offs?
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