Question 6: An experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 20 times, E2 occurred 13 times, and E3 occurred 17 times. Assign probabilities to the outcomes. What method did you use?
Question 7: A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: P(E1)= .10, P(E2) = .15, P(E3)= .40, and P(E4) = .20. Are these probability assignments valid? Explain.
Question 10:
10. Many students accumulate debt by the time they graduate from college. Shown in the fol- lowing table is the percentage of graduates with debt and the average amount of debt for these graduates at four universities and four liberal arts colleges (U.S. News and World Report, America's Best Colleges, 2008). University % with Debt Amount($) College % with Debt Amount(S) Pace 72 32,980 Wartburg 83 28,758 Iowa State 69 32, 130 Morehouse 94 27,000 Massachusetts 55 11,227 Wellesley 55 10,206 SUNY-Albany 64 11,856 Wofford 49 11,012 a. If you randomly choose a graduate of Morehouse College, what is the probability that this individual graduated with debt? b. If you randomly choose one of these eight institutions for a follow-up study on stu- dent loans, what is the probability that you will choose an institution with more than 60% of its graduates having debt? c. If you randomly choose one of these eight institutions for a follow-up study on student loans, what is the probability that you will choose an institution whose graduates with debts have an average debt of more than $30,000? d. What is the probability that a graduate of Pace University does not have debt? e. For graduates of Pace University with debt, the average amount of debt is $32,980. Considering all graduates from Pace University, what is the average debt per graduate?13. A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Do the data confirm the belief that one design is just as likely to be selected as another? Explain. Number of Design Times Preferred 15 UIAWN - 30 40 1018. To investigate how often families eat at home, Harris Interactive surveyed 496 adults liv- ing with children under the age of 18 (USA Today, January 3, 2007). The survey results are shown in the following table. Number of Number of Family Meals Survey per Week Responses 11 11 30 aUAWNEO 36 36 119 114 7 or more 139 For a randomly selected family with children under the age of 18, compute the following. a. The probability the family eats no meals at home during the week. b. The probability the family eats at least four meals at home during the week. c. The probability the family eats two or fewer meals at home during the week20. Fortune magazine publishes an annual list of the 500 largest companies in the United States. The following data show the five states with the largest number of Fortune 500 companies (The New York Times Almanac, 2006). Number of State Companies New York 54 California 52 Texas 48 Illinois 33 Ohio 30 Suppose a Fortune 500 company is chosen for a follow-up questionnaire. What are the probabilities of the following events? a. Let / be the event the company is headquartered in New York. Find P(N). b. Let T be the event the company is headquartered in Texas. Find P(T). c. Let B be the event the company is headquartered in one of these five states. Find P(B)
