Challenge #2 A lawsuit has been filed against your company by a disgruntled empl
ID: 3154812 • Letter: C
Question
Challenge #2
A lawsuit has been filed against your company by a disgruntled employee. It seems that the bonuses you awarded were flawed and those who were awarded bonuses based on their high transactions only did because they ignored a large percentage of customers who would not have purchased anything. Per the company policy, all customers are to be treated equally. The employees allegedly ignored customers based on gender, ethnicity and age. You cannot afford a lawyer so you are defending yourself in court and based on your knowledge of Statistics, you are going to show the judge that your employees were awarded bonuses correctly.
The court wants to review employees with transactions from 80-99. I believe there are six employees in this category. Please complete the chart below. You must convert each employee’s transaction score and OppVol into a z-score. You then must identify the area (%) that corresponds to the z-score. I need to be able to show my work.
Employee Number
Employee Name
Transaction
z-score
OppVol
z-score
1
Miles Davis
82
1021
2
Sharon King
86
686
3
Beyonce Carter
90
275
4
Jay Z
92
84
5
Little Wayne
94
23
6
Bianka Reid
98
416
For Transaction, use the mean 60.76 and the standard deviation 15.11.
For OppVol, use the mean 385.68 and the standard deviation 380.75.
To make the decision below, the employee must be above 70% of their peers in transactions and over 38% in OppVol. If they exceed both metrics, then the employee does not deserve the bonus.
Did Employee #1 deserve the bonus?
Did Employee #2 deserve the bonus?
Did Employee #3 deserve the bonus?
Did Employee #4 deserve the bonus?
Did Employee #5 deserve the bonus?
Did Employee #6 deserve the bonus?
Did the majority of the employees from the sample deserve the bonus? If yes, you won the case.
Employee Number
Employee Name
Transaction
z-score
OppVol
z-score
1
Miles Davis
82
1021
2
Sharon King
86
686
3
Beyonce Carter
90
275
4
Jay Z
92
84
5
Little Wayne
94
23
6
Bianka Reid
98
416
Explanation / Answer
Solution:
Z score formula is given as below:
Z = (X – mean) / standard deviation
The table is given as below:
Employee Number
Employee Name
Transaction
z-score
Probability
OppVol
z-score
Probability
1
Miles Davis
82
1.405691595
0.920092138
1021
1.668601445
0.952401804
2
Sharon King
86
1.670416942
0.95258155
686
0.788759028
0.78487357
3
Beyonce Carter
90
1.93514229
0.973513581
275
-0.290689429
0.385644429
4
Jay Z
92
2.067504964
0.980656702
84
-0.792330926
0.214083872
5
Little Wayne
94
2.199867637
0.986091856
23
-0.952541037
0.170411332
6
Bianka Reid
98
2.464592985
0.993141552
416
0.079632305
0.531735149
Did Employee #1 deserve the bonus?
Yes
Did Employee #2 deserve the bonus?
Yes
Did Employee #3 deserve the bonus?
Yes
Did Employee #4 deserve the bonus?
No
Did Employee #5 deserve the bonus?
No
Did Employee #6 deserve the bonus?
Yes
Did the majority of the employees from the sample deserve the bonus? If yes, you won the case.
Yes
Employee Number
Employee Name
Transaction
z-score
Probability
OppVol
z-score
Probability
1
Miles Davis
82
1.405691595
0.920092138
1021
1.668601445
0.952401804
2
Sharon King
86
1.670416942
0.95258155
686
0.788759028
0.78487357
3
Beyonce Carter
90
1.93514229
0.973513581
275
-0.290689429
0.385644429
4
Jay Z
92
2.067504964
0.980656702
84
-0.792330926
0.214083872
5
Little Wayne
94
2.199867637
0.986091856
23
-0.952541037
0.170411332
6
Bianka Reid
98
2.464592985
0.993141552
416
0.079632305
0.531735149