Confidence Intervals

| November 18, 2015

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.

Employee Number Employee Name Transaction z-score OppVol z-score

For Transaction, use the mean 70.76 and the standard deviation 18.11.

For OppVol, use the mean 390.68 and the standard deviation 390.75.

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.

1. Did Employee #1 deserve the bonus?
2. Did Employee #2 deserve the bonus?
3. Did Employee #3 deserve the bonus?
4. Did Employee #4 deserve the bonus?
5. Did Employee #5 deserve the bonus?
6. Did Employee #6 deserve the bonus?
7. Did the majority of the employees from the sample deserve the bonus? If yes, you won the case.

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