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Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical. Score Probability A 4 0.090 B 3 0.240 C 2 0.390 D 1 0.160 F 0 0.120 a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.) b. What is the probability of earning at least a B in Professor Sanchez's course? (Round your answer to 3 decimal places.) Probability - c. What is the probability of passing Professor Sanchez's course? (Round your answer to 3 decimal places.) Probability - The manager of a publishing company plans to give a $21,000 bonus to the top 14 percent, $7,000 to the next 28 percent, and $4,000 to the next 9 percent of sales representatives. If the publishing company has a total of 230 sales representatives, what is the expected bonus that the company will pay? Expeded bonus An investor considers investing $15,000 in the stock market. He believes that the probability is 0.20 that the economy will improve, 0.47 that it will stay the same, and 0.33 that it will deteriorate. Further, if the economy improves, he expects his investment to grow to $19,000, but it can also go down to $9,000 if the economy deteriorates. If the economy stays the same, his investment will stay at $15,000. a. What is the expected value of his investment? Expected value _ b. What should the investor do if he is risk neutral? c. Is the decision clear-cut if he is risk averse? No A Yes You have $360,000 invested in a well-diversified portfolio. You inherit a house that is presently worth $220,000. Consider the summary measures in the following table: Investment Expected Return Standard Deviation Old portfolio 7% 14% House 13% 29% The correlation coefficient between your portfolio and the house is 0.34. a. What is the expected return and the standard deviation for your portfolio comprising your old portfolio and the house? (Do not round intermediate calculations. Round your final answers to 2 decimal places.) Expected return Standard deviation b. Suppose you decide to sell the house and use the proceeds of $220,000 to buy risk-free T-bills that promise a 9% rate of return. Calculate the expected return and the standard deviation for the resulting portfolio. [Hint. Note that the correlation coefficient between any asset and the risk-free T-bills is zero.] (Do not round intermediate calculations. Round your final answers to 2 decimal places.) Expected return Standard deviationAt a local community college, 60% of students who enter the college as freshmen go on to graduate. Six freshmen are randomly selected. a. What is the probability that none of them graduates from the local community college? (Do not round intermediate calculations. Round your final answer to 4 decimal places.) Probability b. What is the probability that at most five will graduate from the local community college? (Do not round intermediate calculations. Round your final answer to 4 decimal places.) Probability c. What is the expected number that will graduate? (Round your final answer to 2 decimal places.) Expected numberSixty eight percent of a firm's employees are men. Suppose Four of the firm's employees are randomly selected. a. What is more likely, nding three men and one woman or two men and two women? A Finding two men and two women is more likely. A Finding three men and one woman is more likely. A The probabilities of nding three men and one woman . and two men and two women are the same. b. Do you obtain the same answer as in part a if 74% of the rm's employees had been men? A Yes .finding three men and one woman is more likely. A No .finding three men and one woman is more likely. A Yes .finding two men and two women is more likely. A Yes .the probabilities offinding three men and one woman . and two men and two women are the same. Airline travelers should be ready to be more flexible as airlines once again cancel thousands of flights this summer. The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines (h_ttp://seattlepi.com, July 10, 2008). Suppose the hotline is staffed for 16 hours a day. a. Calculate the average number of calls in a one-hour interval; 30-minute interval; 15-minute interval. (Round your answers to 2 decimal places.) Average Number b. What is the probability of exactly six calls in a 15minute interval? (Do not round intermediate calculations. Round your final answer to 4 decimal places.) c. What is the probability of no calls in a 15-minute interval? (Do not round intermediate calculations. Round your final answer to 4 decimal places.) Probability d. What is the probability of at least two calls in a 15-minute interval? (Do not round intermediate calculations. Round your final answer to 4 decimal places.) ProbabilityA committee of 40 members consists of 30 men and 10 women. A subcommittee consisting of16 randomly selected members will be formed. a. What are the expected number of men and women on the subcommittee? b. What is the probability that at least eight of the members on the subcommittee will be women? (Round your answer to 4 decimal places.)
