Discussion
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:
Year 1
Year 2
Year 3
Year 4
Year 5
Total Number of Volunteers
29
31
23
26
28
Number of Volunteers from the Accounting Department
1
1
1
2
1
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:
- How is the number of members of the Accounting Department who are selected to serve on the grievance committee distributed?
- Using the probability distribution you identified in (1), what is the probability for each of these five years that no members of the Accounting Department have been selected to serve?
- Using the probabilities you identified in (2), what is the probability that no members of the Accounting Department have been selected to serve during the past five years?
- 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?
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.
My post
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
f(0)=
=
=0.6552
For year 2,N=31,r=1 and n=10
f(0)=
=
=0.6774
For year 3,N=23,r=1 and n=10
f(0)=
=
=0.5652
For year 4,N=26,r=2 and n=10
f(0)=
=
=0.3692
For year 5,N=28,r=1 and n=10
f(0)=
=
=0.6429
The probability that no member of the Accounting Department is selected to serve during the past 5 years is
=0.6552*0.6774*0.5652*0.3692*0.6429
=0.0595
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.
- How is the number of members of the Accounting Department who are selected to serve on the grievance committee distributed? From the information provided, we know that the probability distribution is hypergeometric in design as we have dependent trials and the probability of success changes from trial to trial (Anderson, 2020). In addition, from the data, we can assign values to x (number of volunteers from accounting who have been selected), n (number randomly selected each year to serve on the committee), N (total number of volunteers), and r (number of volunteers from the Accounting Department) to solve for f(x).
- Using the probability distribution you identified in (1), what is the probability for each of these five years that no members of the Accounting Department have been selected to serve? By using the HYPGEOM.DIST function in Excel, we can quickly calculate the probabilities for each year that no members of the Accounting Department will be selected based on the information that is provided to us. We see that Year 1 has a 0.6552 probability of no members being selected, Year 2 has 0.6774 probability of no members being selected, Year 3 has 0.5652 probability of no members being selected, Year 4 has 0.3692 probability of no members being selected, and Year 5 has 0.6429 probability of no members being selected.
P(x)=oYear 10.6552Year 20.6774Year 30.5652Year 40.3692Year 50.6429
- Using the probabilities you identified in (2), what is the probability that no members of the Accounting Department have been selected to serve during the past five years? In order to calculate the probability that no members have been selected to serve, we know that each of the calculated probabilities for question 2 are independent of one another, so each year can be multiplied by the others to come up with the 5 year probability. Doing this, we come up with 0.6552*0.6674*0.5652*0.3692*0.6429=0.0595 probability.
P(x)=o5 Year ProbabilityYear 10.65520.0595Year 20.6774Year 30.5652Year 40.3692Year 50.6429
- 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? While it is suspicious that no employees from the Accounting department have ever been selected over the past 5 years, we see the first number that is a blaring statistic is the number of volunteers from the Accounting Department across the 5 years. Simple statistics would follow that their chances are very low to have anyone randomly selected as they have a max number of 2 in year 4, while the other years there is only 1 volunteer.
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