Question

Below represent scores on an exam, each entry one score for one student 40 99 59...

Below represent scores on an exam, each entry one score for one student

40
99
59
98
63
63
64
65
67
35
67
67
68
70
71
71
71
46
72
72
60
73
74
74
74
75
97
75
62
76
76
76
76
76
77
57
77
98
77
63
78
78
78
79
79
80
80
80
80
80
81
81
92
81
93
82
82
83
83
83
83
83
83
83
84
84
84
84
84
85
85
86
86
86
86
86
87
88
88
77
88
52
89
89
86
84
91
90
92
88
93
93
46
93
94
94
94
61
95
96
55
43
44
50
71
77
72
43
44
  1. Estimate the number of students who would get points between 75 and 85 using normal distribution. Does it match with the actual data?
Math   Statistics-And-Probability   
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Answer #1

By calculation using excel formula average and stddev

mean = 76.6330

S.D. = 14.2111

P(75.0 < x < 85.0)=?

This implies that

P(75.0 < x < 85.0) = P(-0.1149 < z < 0.5888) = P(Z < 0.5888) - P(Z < -0.1149)

P(75.0 < x < 85.0) = 0.7220022770715641 - 0.45426219254773315

P(75.0 < x < 85.0) = {0.2677} . By calculation

n = 109

values between 75 to 85 = 38

P(75.0 < x < 85.0) = 0.2569 by actual data

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