What score should be used for the two cut offs

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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

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?

Reference no: EM1316294

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