What are some ways that you can apply probability distributions in your personal life? In a given month for example, how many eggs do you typically buy? Then, how many do you eat compared to the number you throw away because they have expired? If you have collected this data, it might help inform your decision at the grocery store to either buy more, fewer, or even no eggs. Also, while you are at the grocery store, if you know the average milk prices and standard deviation, then you might consider buying a gallon that costs a little more or you might think it is worth the second trip to get it cheaper elsewhere. How might you apply these concepts to business situations? Consider different ways that probability distributions could be applied to materials, labor costs and estimations, sales reports, and so on.

In this Assignment, you will respond to a set of questions that provide real-world examples of how probability distributions can be used to make better decisions, improve performance, and predict outcomes.

**To prepare for this Assignment:**

- Review this week’s Learning Resources.
- Refer to the Academic Writing Expectations for 2000/3000-Level Courses as you compose your Assignment.

By Day 7

**Submit** your responses to the following prompts.

- A market-research firm was hired to determine the percentage of people in a market area who would purchase a client’s magazine if a door-to-door sales campaign were undertaken. The firm stated that 40% would buy if contacted at home. Suppose the marketing company has tried the sales campaign at 300 randomly selected homes. (150–225 words, or 2–3 paragraphs)
- Assuming the market research was done properly and the 40% is representative, how many sales are expected if the publisher attempts to sell to 5,000 homes?
- If the market research was accurate, what is the probability that fewer than 100 individuals will buy? Use the normal approximation to the binomial.
- Suppose that the publisher actually sells the magazine to 70 people out of the 300 contacted. What would you conclude about the market research? About the campaign?

- A steel mill produces alloy sheets used for the bodies of automobiles. The mill produces sheets with an average thickness of 0.517 inches and a standard deviation of 0.037 inches. A new car model requires alloy sheets between 0.495 and 0.525 inches thick. What percentage of the sheets made by the mill will be suitable for the new car model? Explain your answer. (75 words, or 1 paragraph)
- The VP of HR for a large company is interested in the distribution of sick-leave hours for employees at the company. A recent study revealed that the distribution was consistent with a normal model, with a mean of 58 hours per year, and a standard deviation of 14 hours. An office manager of one division believes that during the past year, two of the division’s employees have taken excessive sick leave. One took 74 hours and the other used 90 hours. What would you conclude about the division manager’s claim, and why? (75 words, or 1 paragraph)
- Each month, an American household generates an average of 28 pounds of newspaper for garbage and/or recycling. Assume this is approximately normally distributed and that the standard deviation is 2 pounds. If a household is selected at random, find the probability of it generating between 27–31 pounds per month. (75 words, or 1 paragraph)

**Note: **For each prompt, be sure to reference at least one scholarly source to support your answer. Use the Walden Undergraduate Paper Template, provided in this week’s Learning Resources, to complete this Assignment.

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