Several years ago, management at Tuglar Corporation established a grievance committee composed of employees who volunteered to work toward the amicable resolution of disputes between Tuglar management and its employees. Each year management issue a call for volunteers to serve on the grievance committee, and 10 of the respondents are randomly selected to serve on the committee for the upcoming year.

Employees in the Accounting Department are distressed because no member of their department has served on the Tuglar grievance committee in the past five years. Management has assured its employees in the Accounting Department that the selections have been made randomly, but these assurances have not quelled suspicions that management has intentionally omitted accountants from the committee. The table below summarizes the total number of volunteers and the number of employees from the Accounting Department who have volunteered for the grievance committee in each of the past five years:

In its defense, management has provided these numbers to the Accounting Department. Given these numbers, is the lack of members of the Accounting Department on the grievance committee for the past five years suspicious (i.e., unlikely)? 

Managerial Report

In addressing the issue of whether or not the committee selection process is random, consider the following questions:

1. How is the number of members of the Accounting Department who are selected to serve on the grievance committee distributed?

2. Using the probability distribution you identified in (1), what is the probability for each of these five years that no member of the Accounting Department has been selected to serve?

3. Using the probabilities you identified in (2), what is the probability that no member of the Accounting Department has been selected to serve during the past five years?

4. What is the cause of the lack of Accounting Department representation on the grievance committee over the past five years? What can be done to increase the probability that a member of the Accounting Department will be selected to serve on the grievance committee using the current selection method?

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Year 1 Year 2 Year 3 Year 4 Year 5 Total Number of Volunteers 29 31 23 26 28 Number of Volunteers from the 1 1 1 1 Accounting Department