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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 issues 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:
Total Number of Volunteers
Number of Volunteers from the Accounting Department
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)?
In addressing the issue of whether or not the committee selection process is random, consider the following questions:
Initial post prompt: Your Managerial Report serves as your initial post to the discussion forum. After responding to the requirements posed by the Managerial Report, also provide an example in your career in which you believe one of the lessons learned from the Case has been/could be applicable. Alternatively, if you don’t have/foresee direct experience relevant to your current position, what type of scenario can you anticipate occurring where you can utilize one of the lessons learned from examining this case?
Response post prompt: Consider Managerial Reports posted by two of your peers. One or both of your responses may be to Managerial Reports for a case problem different from your own. Think critically and ask open-ended questions. If you agree, consider their position and expand upon their ideas. Provide an additional perspective. If you disagree, provide your reasoning. Always be professional and courteous in your responses.
Let x represent the members of the Accounting Department who are selected to be a part of Grievance Committee. The selection is from a smaller sample of Accounting Department Personnel who volunteer, given by r. Let the total number of volunteers be N.A sample of 10 needs to be selected so n is 10. This is a hypergeometric distribution.
For year 1,N=29,r=1 and n=10
For year 2,N=31,r=1 and n=10
For year 3,N=23,r=1 and n=10
For year 4,N=26,r=2 and n=10
For year 5,N=28,r=1 and n=10
The probability that no member of the Accounting Department is selected to serve during the past 5 years is
The reason why there is less number of members from Accounting Department in the Grievance Committee is because of low volunteering. If the volunteers from Accounting Department increase, we can have a greater probability of having a member from Accounting Department in the Grievance Committee.
The hypergeometric distribution can be used for sampling problems such as the chance of picking a defective part from a box (without returning parts to the box for the next trial).
Post by classmate 1
This week I chose to do my case study on Case Problem 3 – Grievance Committee at Tuglar Corporation.
P(x)=oYear 10.6552Year 20.6774Year 30.5652Year 40.3692Year 50.6429
P(x)=o5 Year ProbabilityYear 10.65520.0595Year 20.6774Year 30.5652Year 40.3692Year 50.6429
Year 1Year 2 Year 3Year 4Year 5Sum of volunteersTotal number of volunteers2931232628137Number of Volunteers from AD111216Percentage per year0.03450.03230.04350.07690.0357Percentage across 5 years0.0438
From these calculations, we see that for each of the 5 years individually, the highest percentage based on the number of volunteers is 7.69% in Year 4. Also, averaging all the years together we see that there is only a cumulative 4.38% chance that a member of the Accounting department would get selected. With the numbers presented, we can deduce that the cause of the lack of Accounting department representation can be attributed to the lack of volunteers that would increase the percent likelihood of a member of the department being selected. We are not given any more information on the makeup of employment at Tuglar Corporation including the total number of employees, number of employees in each department, number of departments, etc. Therefore, with the information we are given, my suggestion would be to try increasing the number of volunteers to increase the percentage that a person in Accounting would be randomly selected to serve on the committee.
As an imaging professional, there are endless statistics involving probabilities that I can reference. There are probabilities that can be calculated on adverse reactions to radiopharmaceuticals that I use to image an organ/organ system and other drugs that I use daily to initiate a response within the body (ex. Stress testing). Using what I have learned this week, I can be better prepared to evaluate this data, and when needed, make additional calculations
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