Business Analytics Data Analysis & Decision Making, 6th Edition by S. Christian Albright - Test Bank Instant Download - Complete Test Bank With Answers Sample Questions Are Posted Below 1. The mean of the probability distribution is also called the: a. median b. standard deviation c. variance d. …
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Business Analytics Data Analysis & Decision Making, 6th Edition by S. Christian Albright – Test Bank
Instant Download – Complete Test Bank With Answers
Sample Questions Are Posted Below
1. The mean of the probability distribution is also called the:
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2. FMV provides a rational way of making decisions:
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3. The preferred criterion in decision making is.
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4. Expected monetary value (EMV) is:
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5. In decision trees, EMVs are calculated through a ____ process.
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6. There are three types of nodes that are used with the decision trees. They are the:
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7. In decision trees, time:
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8. In decision trees, probabilities are listed on probability branches. These probabilities are ____ events that have already been observed.
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9. In decision trees, monetary values:
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10. In a single-stage decision tree problem, you make ____ first and then all you wait to see a(n) ____.
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11. The solution procedure that was introduced in the book for decision trees is called the:
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12. In making decisions, we choose the decision with the largest expected monetary value at each node.
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13. Decision trees are composed of nodes (circles, squares, and triangles) and branches (lines).
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14. In decision trees, a decision node (a square) is a time when the result of an uncertain event becomes known.
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15. In decision trees, a probability node (a circle) is a time when the decision maker makes a decision.
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16. In decision trees, an end node (a triangle) indicates that the problem is completed; that is, all decisions have been made, all uncertainty has been resolved, and all payoffs/costs have been incurred.
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17. In general, the expected monetary values (EMV) represent possible payoffs.
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18. Expected monetary value is the weighted sum of the possible monetary outcomes.
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19. In decision trees, any branches leading into a node (from the left) have already occurred.
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20. The expected monetary value (EMV) criterion is sometimes referred to as “playing the averages”.
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21. EMV criteria guarantee good outcomes.
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| A department store in a small town is in the process of budget planning and will be building a decision tree to select the best option among its available marketing channels. To estimate the probabilities it will need, it considers a customer base of 1500 individuals, 700 of which are women. Data shows that 240 of the women in this population earn at least $50,000 per year and 300 of the men earn at least $50,000 per year. |
22. What is the probability that a randomly selected individual from this population earns less than $50,000 per year?
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23. The expected monetary value represents a long-run average.
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| 24. Tyson Manufacturing (a maker of industrial products) is interested in marketing a new product. The company must decide whether to manufacture this product essentially on its own or employ a subcontractor to manufacture it. Below are two tables that represent the information related to the estimated probability distribution of the cost of one unit of this product under each alternative.
Cost under “Make” alternative. Cost under “Buy” alternative.
Assuming that Tyson seeks to minimize the expected unit cost of manufacturing of buying the new product, should the company make the new product or buy it from a subcontractor? Show your work.
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25. In a single-stage decision problem, a single decision is made first, and then all uncertainty is resolved.
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| A construction company has obtained a contract for a highway project and will need to lease an additional road grader for a month to fill out its equipment fleet. The company is trying to decide between two different lease options for the grader: 1) lease an older grader for $8,500, or 2) lease a newer grader for $10,000. The newer grader is still under warranty, so the lease cost covers all repair expenses. However, the company would be responsible for any repair expenses if it leases the older grader. The construction company’s maintenance foreman believes there is a 30% chance that there will be no need for repairs with the older grader, but also thinks there is a 45% chance that some repairs ($2,000) could be needed, and a 25% chance that significant repairs ($5,000) might be required. |
| 26. (A) Construct a decision tree to help the company make its decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
(B) What is the best lease option? Why? (C) Suppose the company could hire an experienced mechanic to inspect the old grader to determine the repair cost before the company makes its final decision. If the mechanic is always correct in his assessments, what is the most the company would pay for the inspection?
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The Waco Tire Company (WTC) is considering expanding production to meet possible increases in demand. WTC’s alternatives are to construct a new plant, expand the existing plant, or do nothing in the short run. It will cost them $1 million to build a new facility and $600,000 to expand their existing facility. The market for this particular product may expand, remain stable, or contract. ETC’s marketing department estimates the probabilities of these market outcomes as 0.30, 0.45, and 0.25, respectively. The expected revenue for each alternative is presented in the table below.
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| 27. (A) What is WTC’s payoff if they build a new plant and the market expands?
(B) What is WTC’s payoff if they build a new plant and the market is stable? (C) What is WTC’s payoff if they build a new plant and the market contracts? (D) What is WTC’s payoff if they expand the plant and the market expands? (E) What is WTC’s payoff if they expand the plant and the market is stable? (F) What is WTC’s payoff if they expand the plant and the market contracts? (G) What is WTC’s payoff if they do nothing and the market expands? (H) What is WTC’s payoff if they do nothing and the market is stable? (I) What is WTC’s payoff if they do nothing and the market contracts?
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| A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each pair can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs (in hundreds) during the upcoming season has been assessed by the market research specialists and is presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units.
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| 28. (A) What is the payoff if the store orders 400 footballs and quantity demanded is 400 footballs?
(B) What is the payoff if the store orders 400 footballs and quantity demanded is 500 footballs? (C) What is the payoff if the store orders 400 footballs and quantity demanded is 600 footballs? (D) What is the payoff if the store orders 500 footballs and quantity demanded is 400 footballs? (E) What is the payoff if the store orders 500 footballs and quantity demanded is 500 footballs? (F) What is the payoff if the store orders 500 footballs and quantity demanded is 600 footballs? (G) What is the payoff if the store orders 600 footballs and quantity demanded is 400 footballs? (H) What is the payoff if the store orders 600 footballs and quantity demanded is 500 footballs? (I) What is the payoff if the store orders 600 footballs and quantity demanded is 600 footballs?
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| A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not approve the loan application, the $20,000 will be invested in bonds that earn a 6% annual return. Without additional information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the credit union will lose the $20,000. |
29. Construct a decision tree to help the credit union decide whether or not to make the loan. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
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30. What should the credit union do? What is their expected profit?
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| Ms. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Ms. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.
Distribution of Accident Types and Corresponding Damage Amounts
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31. Determine the payoffs associated with each possible decision and type of accident (cost in dollars).
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The Waco Tire Company (WTC) is considering expanding production to meet possible increases in demand. WTC’s alternatives are to construct a new plant, expand the existing plant, or do nothing in the short run. It will cost them $1 million to build a new facility and $600,000 to expand their existing facility. The market for this particular product may expand, remain stable, or contract. ETC’s marketing department estimates the probabilities of these market outcomes as 0.30, 0.45, and 0.25, respectively. The expected revenue for each alternative is presented in the table below.
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32. Construct a decision tree to identify the course of action that maximizes WTC’s expected profit. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
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33. What course of action is optimal for WTC? What is the expected profit in that case?
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34. A risk profile from PrecisionTree lists:
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35. In a multistage decision problem, decisions and outcomes alternate. That is, a decision maker makes a decision, then some uncertainty is resolved, then the decision maker makes a second decision, then some further uncertainty is resolved, and so on.
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36. A risk profile lists the full probability distribution.
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| A landowner in Texas is offered $200,000 for the exploration rights to oil on her land, along with a 25% royalty on the future profits if oil is discovered. The landowner is also tempted to develop the field herself, believing that the interest in her land is a good indication that oil is present. In that case, she will have to contract a local drilling company to drill an exploratory well on her own. The cost for such a well is $750,000, which is lost forever if no oil is found. If oil is discovered, however, the landowner expects to earn future profits of $7,500,000. Finally, the landowner estimates (with the help of her geologist friend) the probability of finding oil on this site to be 60%. |
| 37. (A) Construct a decision tree to help the landowner make her decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
(B) What should the landowner do? Why? (C) Suppose the landowner is uncertain about the reliability of her geologist friend’s estimate of the probability that oil will be found on her land. If she thinks the probability could be anywhere between 40% and 80%, would that change her decision? (D) Suppose that, in addition to the uncertainty about the probability of finding oil, the landowner is also uncertain about the cost of the exploratory well (could vary +/- 25%) and the future profits (could vary +/- 50%). To which of these variables is the expected value most sensitive? (E) What does the risk profile show about the relative risk levels for the landowner’s two options? (F) Suppose the landowner suspects that she may be a somewhat risk-averse decision maker, because the she doesn’t feel there is as much of a difference between the two options as their expected values would indicate. She consults with a decision analysis expert who asks her to decide between two hypothetical alternatives: 1) a gamble with equal probabilities of winning an amount $X and losing an amount –$X/2, and 2) doing nothing, with a payoff of $0. The point at which she cannot decide between 1) and 2) is when X=$1,500,000. What is her risk tolerance if she uses an exponential utility function to model her preferences? (G) Apply the risk tolerance given in your answer to the previous question to the landowner’s decision tree in (A). What is the optimal decision in this case? What is the resulting certainty equivalent? (H) If the landowner could hire an expert geologist prepare a report to help her make her decision, what is the most that information could be worth? Assume the geologist’s information is perfectly reliable.
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The Waco Tire Company (WTC) is considering expanding production to meet possible increases in demand. WTC’s alternatives are to construct a new plant, expand the existing plant, or do nothing in the short run. It will cost them $1 million to build a new facility and $600,000 to expand their existing facility. The market for this particular product may expand, remain stable, or contract. ETC’s marketing department estimates the probabilities of these market outcomes as 0.30, 0.45, and 0.25, respectively. The expected revenue for each alternative is presented in the table below.
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38. Generate a risk profile for each of WTC’s possible decisions in this problem. Characterize the differences in risk for the different options.
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| A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each pair can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs (in hundreds) during the upcoming season has been assessed by the market research specialists and is presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units.
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39. Generate a risk profile for each possible decision in this problem. Would this have any impact on your decision?
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40. Which sensitivity analysis chart is most useful for seeing how the optimal decision changes as selected inputs vary?
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41. PrecisionTree tornado and spider charts are:
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42. ____ can be used to determine which input variables have the most impact on the expected value in a decision problem.
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43. Tornado charts and spider charts can be used to determine which input variables have the most impact on the expected value in a decision problem.
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44. A strategy region chart is useful for seeing whether the decision changes over the range of the input variable.
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45. A risk profile is a chart that represents the probability distribution of monetary outcomes for any decisions.
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| A recent MBA graduate is considering an offer of employment at a biotech company, where she has been offered stock options as part of her compensation package. The options give her the right, but not the obligation, to buy 2500 shares of stock either one year from now or two years from now at a price of $50, which is the current market price of the stock. If the price of the stock has risen above $50 at either time, she can buy 2500 shares at $50 and then immediately sell at the current price, thereby making a risk-free profit. On the other hand, if the price of the stock has dropped below $50, she will not exercise the option because it is “out of the money” and she would loose money. Based on historical market information, she estimates that the stock price in the first year will either go up by 25% from its current price, with probability of 0.55, or it will go down by 15%, with probability of 0.45. In either case, she can exercise the options or wait to see what will happen in the second year. If she decides to wait, the in the second year, the stock price will again go up or down by the same amounts and with the same probabilities, starting from either the “up” or “down” price at the end of the first year. |
| 46. (A) Construct a decision tree to help her model her option decision making. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
(B) What is the optimal decision making policy regarding the options in all possible scenarios over the next two years? (C) What is the expected value of the stock options? Ignore the time value of money (assume no discounting of future payoffs) (D) If her estimates of the increases/decreases or probabilities are inaccurate, could the options have a negative EMV?
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| The owner of a radio station in a rapidly growing community in central Texas is about to begin operations and must decide what type of program format to offer. She is considering three formats; rock, country, and rap. The number of listeners for a particular format will depend on the type of potential audience that is available. Income from advertising depends on the number of listeners the station has. Three broad categories of audience type can be described as A1, A2, and A3. The rock music format draws mainly for the A1 listener, the country music format draws mainly from the A2 listener and the rap music format draws mainly from the A3 listener. The station owner does not know which type of audience will dominate the community once its growth has stabilized. Probabilities have been assigned to the potential dominant audience, based on the community growth that has already occurred in this area. Since she wants to begin building an image now, the decision as to which format to adopt must be made in an environment of uncertainty. The station owner has been able to construct the following payoff table, in which the entries are average monthly revenue in thousands of dollars.
Audience
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47. The station is most uncertain about the average monthly revenue associated with the rock format and an A1 audience. Construct a strategy region chart for this input variable with a possible range from $85,000 to $200,000. Does the optimal decision to select the country format change at any point in this range?
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48. As the average monthly revenue associated with the rock format and an A1 audience varies between $85,000 to about $140,000, what happens to the maximum expected revenue? Briefly explain why.
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49. As the average monthly revenue associated with the rock format and an A1 audience varies between about $142,500 and $200,000, what happens to the maximum expected revenue? Briefly explain why.
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| Ms. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Ms. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.
Distribution of Accident Types and Corresponding Damage Amounts
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50. Generate a statistical summary and risk profile for each of Mrs. Rich’s possible decisions. Does this information impact her decision?
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51. Perform a sensitivity analysis on the optimal decision and summarize your findings. Vary the probability of being in an accident from 0% to 10%, the insurance premium from $50 to $300, and the deductible amount from $0 to $600. In response to which model inputs is the expected total cost value most sensitive?
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| 52. Using a strategy region graph, determine what impact, if any, the probability of being in an accident has on her decision. Briefly explain your answer
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| 53. Using a strategy region graph, determine what impact, if any, the insurance premium cost has on her decision. Briefly explain your answer
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| 54. Using a strategy region graph, determine what impact, if any, the insurance deductible amount has on her decision. Briefly explain your answer
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55. Why is there a kink in the line for the “Buy Insurance” line in the above strategy region chart?
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56. What is Bayes’ Rule?
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57. The expected value of sample information (EVSI) is equal to:
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58. The expected value of perfect information (EVPI) is equal to:
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59. Bayes’ rule can be used for updating the probability of an uncertain outcome after observing the results of a test or study.
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60. Bayes’ is useful in determining the value of perfect information (EVPI).
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| A department store in a small town is in the process of budget planning and will be building a decision tree to select the best option among its available marketing channels. To estimate the probabilities it will need, it considers a customer base of 1500 individuals, 700 of which are women. Data shows that 240 of the women in this population earn at least $50,000 per year and 300 of the men earn at least $50,000 per year. |
61. If a randomly selected individual is observed to earn at least $50,000 per year, what is the probability that this person is a man?
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62. If a randomly selected individual is observed to earn less than $50,000 per year, what is the probability that this person is a woman?
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| A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not approve the loan application, the $20,000 will be invested in bonds that earn a 6% annual return. Without additional information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the credit union will lose the $20,000. |
63. Suppose that an actual (not perfectly reliable) credit report has the following characteristics based on historical data; in cases where the customer did not default on the approved loan, the probability of receiving a favorable recommendation on the basis of the credit investigation was 80%, while in cases where the customer defaulted on the approved loan, the probability of receiving a favorable recommendation on the basis of the credit investigation was 25%. Given this information, what are the posterior probabilities that an earthquake will and will not occur, given the geologists predictions?
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| A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each season on a program that turns out to be a flop, and of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops. |
64. Suppose that an actual (not perfectly reliable) market research report has the following characteristics based on historical data: if the program is actually going to be a hit, there is a 90% chance that the market researchers will predict the program to be a hit, and if the program is actually going to be a flop, there is a 20% chance that the market researchers will predict the program to be a hit. Given this information, what are the posterior probabilities that a show will be a hit or a flop, given the market research report?
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| Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this prospect; the metallurgical properties of the ore and the net price (market price minus mining and transportation costs) of the ore in the future.
The metallurgical properties of the ore would be classified as either “high grade” or “low grade”. Southport’s geologists have estimated that there is a 70% chance that the ore will be “high grade”, and otherwise, it will be “low grade”. Depending on the net price, both ore classifications could be commercially successful. The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport’s economists have simplified the continuous distribution of possible prices into a two-outcome discrete distribution (“high” or “low” net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in millions of dollars), are summarized below.
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65. Since the core test can only sample a small part of the mine, Southport’s geologists believe it is somewhat unrealistic to view it as a perfectly reliable test. Based on similar tests they have conducted in the past, they believe that if the metallurgical properties of the ore are actually High Grade, then the probability that this test will return “favorable” results is 0.95. If the metallurgical properties are Low Grade, the probability that this test will return “favorable” results is only 0.25. Otherwise, the test results will be considered “unfavorable”. Given this information, what are the posterior probabilities that the ore will be a High Grade and Low Grade, given the core test report?
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66. Which of the following statements are true?
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67. The expected value of perfect information (EVPI) is the difference between the EMV with perfect information and the EMV with no additional information.
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| The owner of a radio station in a rapidly growing community in central Texas is about to begin operations and must decide what type of program format to offer. She is considering three formats; rock, country, and rap. The number of listeners for a particular format will depend on the type of potential audience that is available. Income from advertising depends on the number of listeners the station has. Three broad categories of audience type can be described as A1, A2, and A3. The rock music format draws mainly for the A1 listener, the country music format draws mainly from the A2 listener and the rap music format draws mainly from the A3 listener. The station owner does not know which type of audience will dominate the community once its growth has stabilized. Probabilities have been assigned to the potential dominant audience, based on the community growth that has already occurred in this area. Since she wants to begin building an image now, the decision as to which format to adopt must be made in an environment of uncertainty. The station owner has been able to construct the following payoff table, in which the entries are average monthly revenue in thousands of dollars.
Audience
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68. What format is optimal? What is the expected profit in that case?
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| A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not approve the loan application, the $20,000 will be invested in bonds that earn a 6% annual return. Without additional information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the credit union will lose the $20,000. |
69. Should the credit union purchase the report if it costs $150?
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| Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this prospect; the metallurgical properties of the ore and the net price (market price minus mining and transportation costs) of the ore in the future.
The metallurgical properties of the ore would be classified as either “high grade” or “low grade”. Southport’s geologists have estimated that there is a 70% chance that the ore will be “high grade”, and otherwise, it will be “low grade”. Depending on the net price, both ore classifications could be commercially successful. The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport’s economists have simplified the continuous distribution of possible prices into a two-outcome discrete distribution (“high” or “low” net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in millions of dollars), are summarized below.
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70. What should the Southport do? What is their expected profit?
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71. Should Southport conduct the imperfect core test if it costs $250,000?
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72. When the lines for two alternatives cross on a strategy region chart, this shows:
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73. In the nomenclature of Bayes’ Rule, which of the following are probabilities that are conditioned on information that is obtained?
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74. Prior probabilities are sometimes called likelihoods, the probabilities that are influenced by information about the outcome of an earlier uncertainty.
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75. The expected value of sample information (EVSI) is the difference between the EMV we can obtain with sample information and the EMV we can obtain without information.
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76. The expected value of perfect information (EVPI) is irrelevant concept since perfect information is almost never available at any price.
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| A nuclear power company is deciding whether to build a nuclear plant at Chico Canyon or at Pleasantville. The cost of building the power plant is $14 million at Chico and $20 million at Pleasantville. If the company builds at Chico, however, and an earthquake occurs at Chico during the next 5 years, construction will be terminated and the company will lose $14 million (and will still have to build a power plant at Pleasantville). Without further information, the company believes there is a 20% chance that an earthquake will occur at Chico during the next 5 years. |
| 77. (A) Construct a decision tree to help the power company decide what to do. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
(B) Where should the power company build the plant? What is the expected cost? (C) Suppose that a geologist (and his team) can be hired to analyze the fault structure at Chico Canyon. He will either predict whether an earthquake will occur or not. If the geologist is perfectly reliable, what is the most the company should be willing to pay for his services? (D) Suppose that an actual (not perfectly reliable) geologist can be hired to analyze the earthquake risk. The geologist’s past record indicates that he will predict an earthquake on 90% of the occasions for which an earthquake will occur and no earthquake on 85% of the occasions for which an earthquake will not occur. Given this information, what are the posterior probabilities that an earthquake will and will not occur, given the geologists predictions? (E) Should the company hire the geologist if his fee is $1.5M?
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| A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each pair can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs (in hundreds) during the upcoming season has been assessed by the market research specialists and is presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units.
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78. Construct a decision tree to identify the buyer’s course of action that maximizes the expected profit earned by the chain from the purchase and subsequent sale of footballs in the coming year.
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79. What is the optimal strategy for order quantity, and what is the expected profit in that case?
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| The following is a payoff table giving profits for various situations:
States of Nature
The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2 respectively. |
80. What are the expected payoffs for the three alternatives?
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81. What else might one consider in choosing from among these alternatives?
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| The owner of a radio station in a rapidly growing community in central Texas is about to begin operations and must decide what type of program format to offer. She is considering three formats; rock, country, and rap. The number of listeners for a particular format will depend on the type of potential audience that is available. Income from advertising depends on the number of listeners the station has. Three broad categories of audience type can be described as A1, A2, and A3. The rock music format draws mainly for the A1 listener, the country music format draws mainly from the A2 listener and the rap music format draws mainly from the A3 listener. The station owner does not know which type of audience will dominate the community once its growth has stabilized. Probabilities have been assigned to the potential dominant audience, based on the community growth that has already occurred in this area. Since she wants to begin building an image now, the decision as to which format to adopt must be made in an environment of uncertainty. The station owner has been able to construct the following payoff table, in which the entries are average monthly revenue in thousands of dollars.
Audience
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82. Construct a decision tree to help the station identify its optimal format. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
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| A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not approve the loan application, the $20,000 will be invested in bonds that earn a 6% annual return. Without additional information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the credit union will lose the $20,000. |
83. The bank can thoroughly investigate the customer’s credit record and obtain a favorable or unfavorable recommendation. If the credit report is perfectly reliable, what is the most the credit union should be willing to pay for the report?
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| A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each season on a program that turns out to be a flop, and of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops. |
84. Construct a decision tree to help the television network identify the strategy that maximizes its expected profit in responding to a newly proposed television program. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
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85. What should the network do? What is their expected profit?
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86. The network can conduct market research to determine whether a program will be a hit or a flop. If the market research report is perfectly reliable, what is the most the network should be willing to pay for it?
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| Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this prospect; the metallurgical properties of the ore and the net price (market price minus mining and transportation costs) of the ore in the future.
The metallurgical properties of the ore would be classified as either “high grade” or “low grade”. Southport’s geologists have estimated that there is a 70% chance that the ore will be “high grade”, and otherwise, it will be “low grade”. Depending on the net price, both ore classifications could be commercially successful. The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport’s economists have simplified the continuous distribution of possible prices into a two-outcome discrete distribution (“high” or “low” net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in millions of dollars), are summarized below.
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87. Construct a decision tree to help Southport identify the strategy that maximizes its expected profit for this investment. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
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88. Suppose that Southport could consider another alternative – postponing the go/no-go decision on the new venture and drilling for a core sample of the ore to determine with complete certainty its metallurgical property. How much should Southport be willing to pay for the core sample?
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89. The expected value of perfect information (EVPI) is the most the decision maker would be willing to pay for the sample information.
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90. Should the network purchase the report if it costs $160,000?
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91. Mathematically, the utility function for risk adverse individuals is said to be ____ and/or ____.
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92. With regard to decision making, most individuals are ____.
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93. Exponential utility has an adjustable parameter called risk tolerance. The risk tolerance parameter measures:
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94. If x is a monetary value (a payoff if positive, a cost if negative), U(x) the utility of this value, and R > 0 is the risk tolerance, then the function U(x) = 1 – is called a(n):
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95. Utility functions are mathematical functions that transform monetary values – payoffs and costs – into ____.
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96. Rational decision makers are never willing to violate the expected monetary value (EMV) maximization criterion when large amounts of money are at stake.
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97. Utility function is a function that encodes a person’s or company’s feelings toward risk.
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98. The certainty equivalent is the certain dollar amount a risk-averse decision maker would accept in order to avoid a gamble altogether.
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99. For a risk averse decision maker, the certainty equivalent is less than the expected monetary value (EMV).
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| An investor has $25,000 in assets and faces a difficult choice between two investments. If he invests in the first opportunity there is a 70% chance that he will increase his assets by $75,000 and a 30% chance that he will increase his assets by $20,000. If he invests in the second option there is a 40% chance that he will increase his assets by $150,000 and a 60% chance that he will increase his assets by $5,000. |
| 100. (A) Construct a decision tree to help the investor make his decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
(B) What is the best choice for the investor? Why? (C) Suppose that investor has an exponential utility function for final assets with a risk tolerance parameter equal to $60,000. Which investment opportunity will he prefer in this case? What is his certainty equivalent?
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| Suppose that a decision maker’s risk attitude toward monetary gains or losses x given by the utility function U(x) = |
101. Show that this decision maker is indifferent between gaining nothing and entering a risky situation with a gain of $80,000 (probability 1/3) and a loss of $10,000 (probability 2/3).
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102. If there is a 10% chance that one of the decision maker’s family heirlooms, valued at $5,000, will be stolen during the next year, what is the most that she would be willing to pay each year for an insurance policy that completely covers the potential loss of her cherished items?
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| Ms. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Ms. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.
Distribution of Accident Types and Corresponding Damage Amounts
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103. Construct a decision tree to help Ms. Rich decide whether or not to purchase insurance. Note that the tree should minimize Ms. Rich’s annual expected total cost, including the possible insurance premium, deductible payment, and damage payment. In your tree, make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
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104. What should Ms. Rich do? What is her expected cost in that case?
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| Suppose that a decision maker’s utility as a function of her wealth, x, is given by U(x) = ln x (the natural logarithm of x). |
105. Is this decision maker risk averse? Explain why or why not.
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106. The decision maker now has $10,000 and two possible decisions. For Alternative 1, she loses $500 for certain (x=$9,500). For Alternative 2, she loses $0 (x=$10,000) with probability 0.9 and loses $5,000 (x=$5,000) with probability 0.10. Which alternative maximizes the expected utility of her net wealth?
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107. The decision maker now has $15,000 and two possible decisions. For decision 1, she loses $1,000 for certain. For decision 2, she loses $0 with probability 0.9 and loses $4,000 with probability 0.10. Which decision maximizes the expected utility of her net wealth?
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Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
