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.

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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?)