Assignment:
Question 1. How would you describe "probability" from a Statistics for Business perspective to a person that has limited exposure to statistics?
Question 2. Suppose you are rolling 2 dice. What would be the probability of getting 7?
Question 3. An airline would like to know the probability of a piece of passenger's luggage weighing more than 40 pounds. To learn this probability, a baggage handler picks off every 20th bag from the conveyor and weighs it. Do you think these data allow the airline to use the Law of Large Numbers eventually to learn P(luggage weighs more than 40 pounds)?
Question 4. A basketball team is down by 2 points with only a few seconds remaining in the game. There's a 50% chance that the team will be able to make a 2-point shot and tie the game, compared to a 30% chance that it will make a 3-point shot and win. If the game ends in a tie, the game continues to overtime. In overtime, the team has a 50% chance of winning. What should the coach do, go for the 2-point shot or the 3-point shot? Be sure to identify any assumptions you make.
Question 5. A pharmaceutical company has developed a diagnostic test for a rare disease. The test has sensitivity 0.99 (the probability of testing positive among people with the disease) and specificity 0.995 (the probability of testing negative among people who do not have the disease). What other probability must the company determine in order to find the probability that a person who tests positive is in fact healthy?
Question 6. Some electronic devices are better used than new: The failure rate is higher when they are new than when they are six months old. For example, half of the personal music players of a particular brand have a flaw. If the player has the flaw, it dies in the first six months. If it does not have this flaw, then only 10% fail in the first six months. Yours died after you had it for three months. What are the chances that it has this flaw?
Question 7. A contractor built 30 similar homes in a suburban development. The homes have comparable size and amenities, but each has been sold with features that customize the appearance, landscape, and interior. The contractor expects the homes to sell for about $450,000. He expects that one-third of the homes will sell either for less than $400,000 or more than $500,000.
- Would a normal model be appropriate to describe the distribution of sale prices?
- What data would help you decide if a normal model is appropriate? (You cannot use the prices of these 30 homes; the model is to describe the prices of as-yet-unsold homes.)
Question 8. What normal model has properties that are consistent with the intuition of the contractor? An accounting firm assists small businesses file annual tax forms. It assigns each new client to a CPA at the firm who specializes in companies of that type and size. For instance, one CPA specializes in boutique clothing retailers with annual sales of about $2 million. To speed the process, each business submits a preliminary tax form to the accounting firm.
- Would a normal model be useful to describe the total size of adjustments when a CPA reviews the preliminary tax forms? (For example, suppose the preliminary form claims that the business owes taxes of $40,000. If form completed by the CPA says the tax obligation is $35,000, then the adjustment is - $5,000.)
- What data would help you decide if a normal model is appropriate? (You cannot use data from the current year; those data are not yet available.)
- If the average adjustment obtained by the CPA who specializes in clothing retailers is - $7,000 (i.e., $7,000 less than indicated on the preliminary form), then what SD implies that all but a few business end up with lower taxes after the work of these accountants? (Assume a normal model for this question.)
- Would a normal model be useful to describe the total size of adjustments for all of the CPAs at this accounting firm?