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
|
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
|
|
|
|
|
|
|
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?