Can you help me with problem 5.7

180 CHAPTER 5 | Discrete Probability Distributions a. How many fliers do you think the automobile dealership sent out? a. Calculate the expected number of mortgages approved per week. b. Using your answer to (a) and the probabilities listed on the flier, b. Calculate the standard deviation. what is the expected value of the prize won by a prospective c. What is the probability that there will be more than one com- customer receiving a flier? mercial mortgage approved in a given week? Using your answer to (a) and the probabilities listed on the flier, what is the standard deviation of the value of the prize won by a 5.7 You are trying to develop a strategy for investing in two differ- prospective customer receiving a flier? ent stocks. The anticipated annual return for a $1,000 investment d. Do you think this is an effective promotion? Why or why not? in each stock under four different economic conditions has the fol- lowing probability distribution: 5.4 In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player Returns wins or loses his or her bet. For example, the player can bet $1 that the sum will be under 7-that is, 2, 3, 4, 5, or 6. For this bet, Probability Economic Condition Stock X Stock Y the player wins $1 if the result is under 7 and loses $1 if the outcome D.1 Recession -50 - 100 equals or is greater than 7. Similarly, the player can bet $1 that the sum will be over 7-that is, 8, 9, 10, 1 1, or 12. Here, the player wins Slow growth 20 50 0.4 $1 if the result is over 7 but loses $1 if the result is 7 or under. A Moderate growth 100 130 third method of play is to bet $1 on the outcome 7. For this bet, the Fast growth 150 200 player wins $4 if the result of the roll is 7 and loses $1 otherwise. a. Construct the probability distribution representing the different Calculate the outcomes that are possible for a $1 bet on under 7. a. expected return for stock X and for stock Y. b. Construct the probability distribution representing the different b. standard deviation for stock X and for stock Y. outcomes that are possible for a $1 bet on over 7. . Would you invest in stock X or stock Y? Explain. . Construct the probability distribution representing the different outcomes that are possible for a $1 bet on 7. 5.8 You plan to invest $1,000 in a corporate bond fund or in a d. Show that the expected long-run profit (or loss) to the player is common stock fund. The following table presents the annual return the same, no matter which method of play is used. (per $1,000) of each of these investments under various economic conditions and the probability that each of those economic condi- 5.5 The number of arrivals per minute at a bank located in the tions will occur. central business district of a large city was recorded over a period of 200 minutes, with the following results: Economic Corporate Common Arrivals Frequency Probability Condition Bond Fund Stock Fund 0.01 Extreme recession -300 -999 14 31 0.09 Recession -70 -300 47 0.15 Stagnation 30 -100 41 0.35 Slow growth 60 100 29 0.30 Moderate growth 100 150 0.10 High growth 120 350 10 Calculate the a. expected return for the corporate bond fund and for the common stock fund. a. Calculate the expected number of arrivals per minute. b. standard deviation for the corporate bond fund and for the com- b. Calculate the standard deviation. mon stock fund. . What is the probability that there will be fewer than two arrivals c. Would you invest in the corporate bond fund or the common in a given minute? stock fund? Explain. 5.6 The manager of the commercial mortgage department of a d. If you chose to invest in the common stock fund in (c), what do large bank has collected data during the past two years concern- you think about the possibility of losing $999 of every $1,000 ing the number of commercial mortgages approved per week. The invested if there is an extreme recession? results from these two years (104 weeks) are as follows: Number of Commercial Mortgages Approved Frequency 13