Question

Using excel or statcato, stack all ten columns together into a single column. Once you have all 300 grades in a single column, calculate:

   •   The average numeric grade for all 300 students

   •   The standard deviation for numeric grade for all 300 students

   •   If we were to assume the population of grades was normally distributed (which it certainly isn’t) calculated the probability that an individual would have a final grade higher than a 90.

   •   Again, assuming normality, calculate the probability that an individual was have a final grade higher than 80.

A
A
F
F
B-
B
B-
B
A
F
F
A
B
A
B
C
B
B
A
B+
B-
B+
F
C
A-
C
A
B
B+
B
A-
F
B
C-
A
B+
A
C
A-
A-
A
F
F
D
B+
B
C
A
A
B+
B+
B+
B+
B-
C-
F
A
A
A
A
C
A
B-
B-
D-
C
B
A
D-
F
A
B
B
F
B
A-
F
A
B
F
A
C
A
A-
C
B+
A
A-
B
B-
B
C
A-
C-
F
A-
B
B
B+
A-
A
A
C
B
A-
B-
A
A
A-
F
B
A
A-
C+
F
F
A-
A
B
A
F
A
C+
B+
C
B
A
B+
A-
A
B
B-
B
F
A
B
B+
A
A
C+
A-
B+
A
F
A
B
C
A
B+
F
B
B
A
B+
B+
B
B
C+
B
B+
D+
C+
B
F
B
A-
A
A
A
C+
F
B-
C+
D
A
F
A-
B
F
A-
A-
A
B+
A
B
C+
B
A
B
A
B-
B+
B-
A
C-
C
C
B
A
B
A-
C
A-
B
F
B-
C+
A
C+
C-
B
A
A
C
A-
A
B
A
C
A-
B
B
F
A-
A
A
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B
A-
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F
B
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C
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A-
A
B
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A
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A
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C
F
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A
F
A
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B
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C
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F
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D+
F
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A-
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A-
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A-
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A
D+
A-

95
96
94
58
67
94
89
88
97
76
50
94
61
63
78
90
79
81
98
64
86
91
92
95
85
79
89
88
95
92
94
65
40
80
93
81
95
89
91
88
96
58
88
77
98
91
97
79
93
94
92
91
61
74
90
89
80
95
96
91
80
95
90
85
77
58
98
99
100
97
95
89
85
86
71
78
88
94
72
68
97
83
88
62
89
93
42
98
89
59
88
79
95
93
80
92
96
93
89
86
96
99
93
77
59
93
89
88
92
93
88
97
80
89
93
86
95
97
93
35
68
99
94
84
58
67
93
98
88
98
88
85
84
92
80
87
95
90
93
98
93
91
89
64
96
87
91
95
96
84
89
88
97
65
97
88
79
95
92
58
75
83
95
91
92
87
89
84
89
92
60
86
87
46
91
93
95
96
98
83
93
98
83
75
97
59
93
89
47
94
86
91
92
95
88
83
87
95
88
96
93
79
85
95
78
80
81
89
97
89
89
95
94
88
68
85
83
95
84
78
89
87
98
80
93
96
88
97
82
93
43
87
54
93
95
97
93
87
94
94
92
90
95
68
83
88
93
95
89
97
93
79
87
95
97
89
96
91
98
86
86
89
56
68
91
98
64
97
96
95
89
88
85
79
95
96
94
57
99
79
95
97
96
77
75
60
87
67
63
84
95
96
91
89
93
95
69
86
61
53

Answer 1

Note : The following calculations are based on the assumption that it is a sample of 300 grades. If it is a population and not a sample then use the Excel function stdev.p for standard deviation and the calculations will change for parts 2,3,4

1) Average Numeric Grade = 85.6267    (Using Excel function average)
     
2) Assuming this is a sample and not a population we use Excel function stdev.s fro standard deviation calculation    
Standard Deviation for numeric grade = 12.524    
     
3) Since population is assumed normal, we find the probability using Excel function NORM.DIV    
Let X be the grade    
To find P(X > 90)    
P(X > 90) = 1 - P(X ≤ 90)    
P(X > 90) = 1- NORM.DIST(90, 85.6267, 12.524, TRUE)    
                    = 0.3635    
Probability that an individual would have a final grade higher than a 90 = 0.3635    
     
4) To find P(X > 80)    
P(X > 80) = 1 - P(X ≤ 80)    
P(X > 80) = 1- NORM.DIST(80, 85.6267, 12.524, TRUE)    
                    = 0.6734    
Probability that an individual would have a final grade higher than 80 = 0.6734