To compute probability value using normal distribution
Robinson & Associates does employment screening for large companies in southern California. It typically follows two-step process. First potential applicants are assumed a test that covers basic knowledge and intelligence. If applicants score among a certain ranges, they are called in for an interview. If they score under a certain point they are sent a rejection letter. If applicants score overhead a certain point, they are sent straight to the client's human resources office without the interview. Recently Robinson & Associates instigated working with a new client and formulated a new test just for this company. Thirty people were specified the test which is theoretical to produce scores that are distributed according to a bell-shaped distribution. The following data reproduce 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 and Associates has in the past issued a rejection letter with no interview to the lower 16% taking the test. They as well send the upper 2.5% directly to the company without an interview. Everybody else is interviewed. Based on the data as well as the assumption of a bell-shaped distribution, what score must be used for the two cut-offs?