What is the probability for: a.) Randomly selecting a person being a male in Gra
ID: 3206934 • Letter: W
Question
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?
ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Gr 1 62.9 1.104 57 34 85 8 0 5.7 0 M E 2 27.2 0.879 31 52 80 7 0 3.9 0 M B 3 34.9 1.127 31 30 75 5 1 3.6 1 F B 4 64.6 1.134 57 42 100 16 0 5.5 1 M E The column labels in the table mean: 5 49.2 1.026 48 36 90 16 0 5.7 1 M D ID – Employee sample number Salary – Salary in thousands 6 77.7 1.160 67 36 70 12 0 4.5 1 M F Age – Age in years Performance Rating - Appraisal rating (employee evaluation score) 7 41.2 1.029 40 32 100 8 1 5.7 1 F C Service – Years of service (rounded) Gender – 0 = male, 1 = female 8 22 0.956 23 32 90 9 1 5.8 1 F A Midpoint – salary grade midpoint Raise – percent of last raise 9 73.4 1.095 67 49 100 10 0 4 1 M F Grade – job/pay grade Degree (0= BSBA 1 = MS) 10 23.9 1.039 23 30 80 7 1 4.7 1 F A Gender1 (Male or Female) Compa - salary divided by midpoint 11 21.8 0.947 23 41 100 19 1 4.8 1 F A 12 60.8 1.066 57 52 95 22 0 4.5 0 M E 13 41.8 1.044 40 30 100 2 1 4.7 0 F C 14 23.3 1.012 23 32 90 12 1 6 1 F A 15 24.6 1.070 23 32 80 8 1 4.9 1 F A 16 47.4 1.186 40 44 90 4 0 5.7 0 M C 17 66.6 1.169 57 27 55 3 1 3 1 F E 18 34.8 1.124 31 31 80 11 1 5.6 0 F B 19 24.5 1.065 23 32 85 1 0 4.6 1 M A 20 35.9 1.159 31 44 70 16 1 4.8 0 F B 21 77.1 1.150 67 43 95 13 0 6.3 1 M F 22 58.9 1.228 48 48 65 6 1 3.8 1 F D 23 23.8 1.036 23 36 65 6 1 3.3 0 F A 24 55.1 1.147 48 30 75 9 1 3.8 0 F D 25 24.6 1.069 23 41 70 4 0 4 0 M A 26 24.1 1.047 23 22 95 2 1 6.2 0 F A 27 45.3 1.133 40 35 80 7 0 3.9 1 M C 28 75.2 1.122 67 44 95 9 1 4.4 0 F F 29 78.7 1.175 67 52 95 5 0 5.4 0 M F 30 48.3 1.006 48 45 90 18 0 4.3 0 M D 31 24.2 1.050 23 29 60 4 1 3.9 1 F A 32 27.6 0.889 31 25 95 4 0 5.6 0 M B 33 61.2 1.074 57 35 90 9 0 5.5 1 M E 34 27 0.872 31 26 80 2 0 4.9 1 M B 35 23.8 1.036 23 23 90 4 1 5.3 0 F A 36 24.4 1.060 23 27 75 3 1 4.3 0 F A 37 23.5 1.023 23 22 95 2 1 6.2 0 F A 38 61.3 1.075 57 45 95 11 0 4.5 0 M E 39 34.4 1.109 31 27 90 6 1 5.5 0 F B 40 24.7 1.076 23 24 90 2 0 6.3 0 M A 41 45.8 1.145 40 25 80 5 0 4.3 0 M C 42 22.4 0.975 23 32 100 8 1 5.7 1 F A 43 75.6 1.129 67 42 95 20 1 5.5 0 F F 44 61.3 1.075 57 45 90 16 0 5.2 1 M E 45 59.7 1.244 48 36 95 8 1 5.2 1 F D 46 55.1 0.967 57 39 75 20 0 3.9 1 M E 47 63.8 1.119 57 37 95 5 0 5.5 1 M E 48 62.8 1.101 57 34 90 11 1 5.3 1 F E 49 64 1.122 57 41 95 21 0 6.6 0 M E 50 66.3 1.163 57 38 80 12 0 4.6 0 M EExplanation / Answer
Question 1
Solution:
The cross-tabulation for the gender and grade is given as below:
Grade
Total
A
B
C
D
E
F
Gender
F
12
4
2
3
2
2
25
M
3
3
3
2
10
4
25
Total
15
7
5
5
12
6
50
Part a
Here, we have to find P(male and grade E)
P(male and grade E) = 10/50 = 0.20
Required probability = 0.20
Part b
Here, we have to find the probability of person in grade E given that he was a male.
P(grade E given male) = 10/25 = 0.40
Required probability = 0.40
Part c
Results are different because for the above two probabilities, although interested items are same but the sample spaces or reference frames are different. In the first part we calculate the probability of event a and b while in the second part we calculate the probability a given b.
Question 2
Part a
From the given data we have following information
Group Statistics
Gender
N
Mean
Std. Deviation
Std. Error Mean
Salary
M
25
52.7920
17.99231
3.59846
F
25
38.3480
18.28932
3.65786
Here, we have to find 75th percentile of salary for Males.
The Z-score for 75th percentile is given as 0.67449
X = mean + Z*SD
X = 52.7920 + 0.67449*17.99231
X = 64.92763
75th percentile = 64.92763
Grade
Total
A
B
C
D
E
F
Gender
F
12
4
2
3
2
2
25
M
3
3
3
2
10
4
25
Total
15
7
5
5
12
6
50
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