Exam 17: Decision Making

A medical doctor is involved in a $1 million malpractice suit. He can either settle out of court for $250,000 or go to court. If he goes to court and loses, he must pay $825,000 plus $175,000 in court costs. If he wins in court the plaintiffs pay the court costs. Identify the outcomes of this Decision-making problem.

$\text { TABLE 17-6 }$ A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the average amount of time he needed to put in every week studying for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. 16 hours 8 hours 4 hours Easy Exam 40 60 80 Difficult Exam 100 50 0 -Referring to Table 17-6, how many possible courses of action are there?

TABLE 17-5 The following payoff table shows profits associated with a set of 2 alternatives under 3 possible events. $\quad$ $\quad$ $\quad$ $\quad$ $\text {Action }$ Event A B 1 1000 1200 2 500 700 3 300 -200 Suppose that the probability of Event 1 is 0.2, Event 2 is 0.5, and Event 3 is 0.3. -Referring to Table 17-5, what is the coefficient of variation for Action A?

TABLE 17-2 The following payoff matrix is given in dollars. $\quad$ $\quad$ $\quad$ $\quad$ $\text {Action }$ Event A B 1 400 700 2 200 500 Suppose the probability of Event 1 is 0.5 and Event 2 is 0.5. -Referring to Table 17-2, what is the optimal action using the EOL criterion?

TABLE 17-5 The following payoff table shows profits associated with a set of 2 alternatives under 3 possible events. $\quad$ $\quad$ $\quad$ $\quad$ $\text {Action }$ Event A B 1 1000 1200 2 500 700 3 300 -200 Suppose that the probability of Event 1 is 0.2, Event 2 is 0.5, and Event 3 is 0.3. -Referring to Table 17-5, what is the expected profit under certainty (EPUC ) for this problem?

A medical doctor is involved in a $1 million malpractice suit. He can either settle out of court for $250,000 or go to court. If he goes to court and loses, he must pay $825,000 plus $175,000 in court costs. If he wins in court the plaintiffs pay the court costs. Identify the actions of this Decision-making problem.

In a local cellular phone area, company A accounts for 60% of the cellular phone market, while company B accounts for the remaining 40% of the market. Of the cellular calls made with company A, 1% of the calls will have some sort of interference, while 2% of the cellular calls with company B will have interference. If a cellular call is selected at random, what is the probability that it will have interference?

______is a procedure for revising probabilities based upon additional information.

TABLE 17-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the average amount of time he needed to put in every week studying for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. 16 hours 8 hours 4 hours Easy Exam 40 60 80 Difficult Exam 100 50 0 -Referring to Table 17-6, what is the expected monetary value of spending 8 hours per week on average studying for the exam?

TABLE 17-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the average amount of time he needed to put in every week studying for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. 16 hours 8 hours 4 hours Easy Exam 40 60 80 Difficult Exam 100 50 0 -Referring to Table 17-6, what is the opportunity loss of spending 4 hours per week on average studying for the exam when the exam turns out to be easy?

TABLE 17-1 The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature. States A1 A2 A3 1 12 -2 8 2 4 10 5 $\text {where:}$$\quad$$\quad$ $\text {S1 is state of nature 1 }$$\quad$$\text {A1 is action alternative 1}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\text {S2 is state of nature 2}$$\quad$$\text { A2is action alternative 2}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {A3 is action alternative3 }$ -Referring to Table 17-1, if the probability of S1 is 0.5, what is the coefficient of variation for A1?

Blossom's Flowers purchases roses for sale for Valentine's Day. The roses are purchased for $10 a dozen and are sold for $20 a dozen. Any roses not sold on Valentine's Day can be sold for $5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine's Day: 100, 200, or 400 dozen roses. Given 0.2, 0.4, and 0.4 are the probabilities for the sale of 100, 200, or 400 dozen roses, respectively, then the optimal alternative using EMV for selling roses is to buy _____ dozen roses.

In portfolio analysis, the _________is the reciprocal of the return to risk ratio.

The curve for the _____ will show a rapid increase in utility for initial amounts of money followed by a gradual leveling off for increasing dollar amounts.

Blossom's Flowers purchases roses for sale for Valentine's Day. The roses are purchased for $10 a dozen and are sold for $20 a dozen. Any roses not sold on Valentine's Day can be sold for $5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine's Day: 100, 200, or 400 dozen roses. Given 0.2, 0.4, and 0.4 are the probabilities for the sale of 100, 200, or 400 dozen roses, respectively, what is the optimal EOL for buying roses?

Blossom's Flowers purchases roses for sale for Valentine's Day. The roses are purchased for $10 a dozen and are sold for $20 a dozen. Any roses not sold on Valentine's Day can be sold for $5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine's Day: 100, 200, or 400 dozen roses. What is the payoff for buying 200 dozen roses and selling 100 dozen roses at the full price?

At Eastern University, 60% of the students are from suburban areas, 30% are from rural areas, and 10% are from urban areas. Of the students from the suburban areas, 60% are nonbusiness majors. Of the students from the rural areas, 70% are nonbusiness majors. Of the students from the urban areas, 90% are nonbusiness majors. What is the probability that a randomly selected student is a business major?

TABLE 17-5 The following payoff table shows profits associated with a set of 2 alternatives under 3 possible events. $\quad$ $\quad$ $\quad$ $\quad$ $\text {Action }$ Event A B 1 1000 1200 2 500 700 3 300 -200 Suppose that the probability of Event 1 is 0.2, Event 2 is 0.5, and Event 3 is 0.3. -Referring to Table 17-5, what is the optimal action using EOL?

TABLE 17-5 The following payoff table shows profits associated with a set of 2 alternatives under 3 possible events. $\quad$ $\quad$ $\quad$ $\quad$ $\text {Action }$ Event A B 1 1000 1200 2 500 700 3 300 -200 Suppose that the probability of Event 1 is 0.2, Event 2 is 0.5, and Event 3 is 0.3. -Referring to Table 17-5, what is the EOL for Action B?

TABLE 17-3 The following information is from 2 investment opportunities. A B Expected monetary value \ 900 \ 600 Standard deviation 100 50 -Referring to Table 17-3, what is the return to risk ratio for Investment B?