A lawsuit has been filed against your company by a disgruntled employee. It seem

Question

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 90-110. 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.

Employee Number

Employee Name

Transaction

z-score

OppVol

z-score

1

M. Scott

109

1316

2

J. Santiago

105

895

3

M. Clarke

104

659

4

D. Arias

101

653

5

T. Dixon

96

1050

6

A. Reda

95

658

For Transaction, use the mean 39.67 and the standard deviation 9.05.

For OppVol, use the mean 695.86 and the standard deviation 300.80.

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

M. Scott

109

1316

2

J. Santiago

105

895

3

M. Clarke

104

659

4

D. Arias

101

653

5

T. Dixon

96

1050

6

A. Reda

95

658

Explanation / Answer

Follwoing is the completed table:

Since all employees above both metrics so no one is eligible for bonus.

Did the majority of the employees from the sample deserve the bonus? No

Employee Number Employee Name Transaction, x z-score=(x-39.67)/9.05 P(Z<=z) (in %) OppVol, Y z-score=(x-695.86)/300.80 P(Z<=z) (in %) Deserve bonus 1 M. Scott 109 7.66 100 1316 2.06 98.03 No 2 J. Santiago 105 7.22 100 895 0.66 74.54 No 3 M. Clarke 104 7.11 100 659 -0.12 45.22 No 4 D. Arias 101 6.78 100 653 -0.14 44.43 No 5 T. Dixon 96 6.22 100 1050 1.18 88.1 No 6 A. Reda 95 6.11 100 658 -0.13 44.83 No

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