Description
Refer to the Excel file Salary (attached) to address all the questions below:
- What is the probability for:
a.) Randomly selecting a person being a male in Grade E?
b.) Given that we picked a random person and he was a male, what is the probability of being in grade E?
c.) Why the results different?
2. Consider each group (Male and Female separately) and assume the salaries follow a Normal Probability distribution:
a.) What is the top 75th percentile of salary for Males?
b.) What is the top 75th percentile of salary for Females?
c.) What is the probability that a male picked at random makes more than 50K?
d.) What is the probability that a female picked at random makes between 30K and 40K?
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Explanation & Answer
Attached.
ID
Salary
Compa
Midpoint
Age
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
62.9
27.2
34.9
64.6
49.2
77.7
41.2
22
73.4
23.9
21.8
60.8
41.8
23.3
24.6
47.4
66.6
34.8
24.5
35.9
77.1
58.9
23.8
55.1
24.6
24.1
45.3
75.2
78.7
48.3
24.2
27.6
61.2
27
23.8
24.4
23.5
61.3
34.4
24.7
1.104
57
31
31
57
48
67
40
23
67
23
23
57
40
23
23
40
57
31
23
31
67
48
23
48
23
23
40
67
67
48
23
31
57
31
23
23
23
57
31
23
34
52
30
42
36
36
32
32
49
30
41
52
30
32
32
44
27
31
32
44
43
48
36
30
41
22
35
44
52
45
29
25
35
26
23
27
22
45
27
24
0.879
1.127
1.134
1.026
1.160
1.029
0.956
1.095
1.039
0.947
1.066
1.044
1.012
1.070
1.186
1.169
1.124
1.065
1.159
1.150
1.228
1.036
1.147
1.069
1.047
1.133
1.122
1.175
1.006
1.050
0.889
1.074
0.872
1.036
1.060
1.023
1.075
1.109
1.076
Performance Service Gende Raise
Rating
r
85
80
75
100
90
70
100
90
100
80
100
95
100
90
80
90
55
80
85
70
95
65
65
75
70
95
80
95
95
90
60
95
90
80
90
75
95
95
90
90
8
7
5
16
16
12
8
9
10
7
19
22
2
12
8
4
3
11
1
16
13
6
6
9
4
2
7
9
5
18
4
4
9
2
4
3
2
11
6
2
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
5.7
3.9
3.6
5.5
5.7
4.5
5.7
5.8
4
4.7
4.8
4.5
4.7
6
4.9
5.7
3
5.6
4.6
4.8
6.3
3.8
3.3
3.8
4
6.2
3.9
4.4
5.4
4.3
3.9
5.6
5.5
4.9
5.3
4.3
6.2
4.5
5.5
6.3
41
42
43
44
45
46
47
48
49
50
45.8
22.4
75.6
61.3
59.7
55.1
63.8
62.8
64
66.3
1.145
0.975
1.129
1.075
1.244
0.967
1.119
1.101
1.122
1.163
40
23
67
57
48
57
57
57
57
57
25
32
42
45
36
39
37
34
41
38
80
100
95
90
95
75
95
90
95
80
5
8
20
16
8
20
5
11
21
12
0
1
1
0
1
0
0
1
0
0
4.3
5.7
5.5
5.2
5.2
3.9
5.5
5.3
6.6
4.6
Degree Gender
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
M
M
F
M
M
M
F
F
M
F
F
M
F
F
F
M
F
F
M
F
M
F
F
F
M
F
M
F
M
M
F
M
M
M
F
F
F
M
F
M
Gr
E
B
B
E
D
F
C
A
F
A
A
E
C
A
A
C
E
B
A
B
F
D
A
D
A
A
C
F
F
D
A
B
E
B
A
A
A
E
B
A
The column labels in the table mean:
ID – Employee sample number
Salary – Salary in thousands
Age – Age in years
Performance Rating - Appraisal rating (em
Service – Years of service (rounded) Gender – 0 = male, 1 = female
Midpoint – salary grade midpoint
Raise – percent of last raise
Grade – job/pay gra...