The objective of this case study is to be able to compare and contrast the classical and empirical probability approaches to a business setting. Assume a “with replacement” situation for all questions.

Scenario: The Skittles manufacturing plant would like to ensure that the production of Skittles is not skewing over the course of a day at the plant. Refer to the Excel file “MandMs.xlsx” on the first tab entitled “Known Probabilities” to see the settings that are used to create the colors of the “rainbow”. Answer the following questions on that same tab.

1. What is the probability of randomly selecting a red Skittle?
2. What is the probability of randomly selecting 5 red Skittles?
3. What is the probability of randomly selecting a red Skittle and then a purple Skittle?

The general manager at the facility decides to sample 100 Skittles randomly pulled off of a line during the first 10 minutes of the day and records the colors on the second tab of the Excel file entitled “1 Sample of 100 M&Ms”. Include a table on this tab that calculates the probability of each color from this sample. Using these probabilities answer the following questions on that same tab:

1. What is the probability of randomly selecting a red Skittle?
2. What is the probability of randomly selecting 5 red Skittles?
3. What is the probability of randomly selecting a red Skittle and then a purple Skittle?
4. How does this distribution of percentages compare to the manufacturing settings from the first tab?

After this first sample, the GM decides to sample throughout the day in 10-minute increments, while still allowing for employee breaks and lunches. This results in 100 separate samples of 100 M&M’s; on the third table of the Excel file, entitled “100 Samples of 100 M&M’s,” the GM has listed the count of each color of Skittle by 10- minute period (in order). Include a table on this tab that calculates the average probability of each color for the 100 samples. Using these probabilities answer the following questions on that same tab:

1. What is the probability of randomly selecting a red Skittle?
2. What is the probability of randomly selecting 5 red Skittles?
3. What is the probability of randomly selecting a red Skittle and then a purple Skittle?
4. How does this distribution of percentages compare to the single sample percentages calculated on the second tab?
5. How does this distribution of percentages compare to the manufacturing settings from the first tab?

If the GM needs to present his findings to corporate, what should he tell them? (Is the plant maintaining the known settings? Is there anything odd throughout the day? Are there any outliers/problem periods?)

 

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250 words minimum.

Writing a Thoughtful Response
When writing a response, I want you to really focus on how you react to the piece you read. You may be able to answer several of the questions raised below in your response. You should aim to address at least 2. Be thorough and thoughtful. Use quotes to demonstrate.

1. What does the text have to do with you, personally? Your life? Every article we are presented with will, likely, have some connection to the world we live in. What’s the connection here.
2. How much does the text agree or clash with your view of the world, and what you consider right and wrong? Use several quotes as examples of how it agrees with and supports what you think about the world or your experiences, about right and wrong, and about what you think it is to be human.
3. How did you learn, and how much were your views and opinions challenged or changed by this text, if at all? Did the text communicate with you? Why or why not? How did your views change or get strengthened (or perhaps, of why the text failed to convince you). Please do not write “I agree with everything,” since there is likely, at least, a tiny point with which you disagree. Use quotes to illustrate your points of challenge, or where you were persuaded, or where it left you disinterested. The templates in Chapter 4 will be valuable for this.
4. How well does it address things that you, personally, care about and consider important to the world? How does it address things that are important to your family, your community, your ethnic group, to people of your economic or social class or background, or your faith tradition? If not, who does or did the text serve?
5. Reading and writing “critically” does not mean the same thing as “criticizing,” in everyday language (complaining or griping, fault-finding, nit-picking). Your “critique” can and should be positive and praise the text if possible, as well as pointing out problems, disagreements and shortcomings.
6. To sum up, what is your overall reaction to the text? Would you read something else like this, or by this author, in the future or not? Why or why not? To whom would you recommend this text? Why might this text be useful? How does it contribute to the “conversation?”

 

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