Q&A Hero

Q: NARRBEGIN: SA_55_62A 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%.NARREND(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.

Q: A spider chart shows both the range (as a percentage) of the variability of the input variables as well as the resulting changes in the expected value

Q: The expected monetary value (EMV) criterion is sometimes referred to as "playing the averages" and for that reason should only be used for recurring decisions.

Q: For each possible decision and each possible outcome, the payoff table lists the monetary value earned by an organization, where a positive value represents a profit and a negative value represents a loss.

Q: The expected value of perfect information (EVPI) is equal to: a. EMV with posterior information " EMV with prior information b. EMV with free perfect information " EMV with information c. EMV with free perfect information " EMV with no information d. EMV with perfect information " EMV with less than perfect information

Q: When the lines for two alternatives cross on a strategy region chart, this shows: a. A change in which decision alternative is optimal b. The point at which a decision was made c. The point where the rate of change in expected value is zero d. Resolution of the uncertainty about the input variable e. None of these options

Q: Which of these sensitivity analysis charts is most useful in determining whether the optimal decision changes over the range of the input variable? a. Strategy region chart b. Tornado chart c. Spider chart d. All of these options e. None of these options

Q: The solution procedure that was introduced in the book for decision trees is called the: a. folding diagram b. single-stage method c. risk profile method d. precision tree method e. folding back on the tree

Q: In a single-stage decision tree problem, all ___________ are made first and then all ___________ is (are) resolved. a. decisions; uncertainty b. calculations; probabilities c. EMV calculations; posterior probabilities d. likelihoods; posterior probabilities e. prior probabilities; joint probabilities

Q: In decision trees, time: a. is constant b. proceeds from bottom to top c. proceeds from top to bottom d. proceeds from right to left e. proceeds from left to right

Q: All problems related to decision making under uncertainty have three common elements: a. the mean, median, and mode b. the set of decisions, the cost of each decision and the profit that can be made from each decision c. the set of possible outcomes, the set of decision variables and the constraints d. the set of decisions, the set of possible outcomes, and a value model that prescribes results e. None of these options

Q: NARRBEGIN: SA_118_122Southport 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.High Grade metallurgy (p=0.7)Low Grade metallurgy (p=0.3)PricesProbabilityOutcomeProbabilityOutcomeHigh0.8$400.6$20Low0.2-$200.4-$40NARRENDShould Southport conduct the imperfect core test if it costs $250,000?

Q: NARRBEGIN: SA_118_122Southport 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.High Grade metallurgy (p=0.7)Low Grade metallurgy (p=0.3)PricesProbabilityOutcomeProbabilityOutcomeHigh0.8$400.6$20Low0.2-$200.4-$40NARRENDSuppose 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?

Q: NARRBEGIN: SA_118_122Southport 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.High Grade metallurgy (p=0.7)Low Grade metallurgy (p=0.3)PricesProbabilityOutcomeProbabilityOutcomeHigh0.8$400.6$20Low0.2-$200.4-$40NARRENDWhat should the Southport do? What is their expected profit?

Q: NARRBEGIN: SA_104_112Mrs. 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. Mrs. 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 AmountsType of AccidentConditional ProbabilityDamage to CarMinor0.60$200Moderate0.20$1,000Serious0.10$4,000Catastrophic0.10$30,000NARRENDGenerate a statistical summary and risk profile for each of Mrs. Rich's possible decisions. Does this information impact her decision?

Q: NARRBEGIN: SA_102_103 Suppose that a decision maker's risk attitude toward monetary gains or losses x given by the utility function U(x) = NARREND 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).

Q: NARRBEGIN: SA_86_89A 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.Demand (in hundreds)Probability40.3050.5060.20NARRENDFormulate a payoff table that specifies the contribution to profit (in dollars) from the sales of footballs by this chain for each possible purchase decision (in hundreds of pairs) and each outcome with respect to consumer demand.

Q: NARRBEGIN: SA_74_78 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. NARREND (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?

Q: NARRBEGIN: SA_121_124 A continuous random variable X has the probability density function: f(x) = 2, 0 NARREND What is the probability that X is at most 2?

Q: NARRBEGIN: SA_121_124 A continuous random variable X has the probability density function: f(x) = 2, 0 NARREND Find the mean and standard deviation of X.

Q: NARRBEGIN: SA_121_124 A continuous random variable X has the probability density function: f(x) = 2, 0 NARREND What is the distribution of X and what are the parameters?

Q: NARRBEGIN: SA_115_116 A used car salesman in a small town states that, on the average, it takes him 5 days to sell a car. Assume that the probability distribution of the length of time between sales is exponentially distributed. NARREND What is the probability that he will have to wait between 6 and 10 days before making another sale?

Q: NARRBEGIN: SA_112_114 The number of arrivals at a local gas station between 3:00 and 5:00 P.M. has a Poisson distribution with a mean of 12. NARREND Find the probability that the number of arrivals between 3:00 and 5:00 P.M. is at least 10.

Q: NARRBEGIN: SA_104_106 A large retailer has purchased 10,000 DVDs. The retailer is assured by the supplier that the shipment contains no more than 1% defective DVDs (according to agreed specifications). To check the supplier's claim, the retailer randomly selects 100 DVDs and finds six of the 100 to be defective. NARREND (A) Assuming the supplier's claim is true, compute the mean and the standard deviation of the number of defective DVDs in the sample. (B) Based on your answer to (A), is it likely that as many as six DVDs would be found to be defective, if the claim is correct? (C) Suppose that six DVDs are indeed found to be defective. Based on your answer to (A), what might be a reasonable inference about the manufacturer's claim for this shipment of 10,000 DVDs?

Q: NARRBEGIN: SA_79_90 The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. NARREND What is the probability that at most two of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Q: NARRBEGIN: SA_76_78 A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8. NARREND Only 5% of the students taking the test scored higher than what value?

Q: The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.

Q: The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.

Q: The binomial distribution deals with consecutive trials, each of which has two possible outcomes.

Q: Using the standard normal curve, the Z- score representing the 75th percentile is 0.674.