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- A group of medical professionals is considering theconstruction of a private clinic. If the medical de-mand is high (i.e., there is a favorable market for theclinic), the physicians could realize a net profit of$100,000. If the market is not favorable, they couldlose $40,000. Of course, they don’t have to proceedat all, in which case there is no cost. In the absenceof any market data, the best the physicians can guessis that there is a 50–50 chance the clinic will be suc-cessful. Construct a decision tree to help analyze thisproblem. What should the medical professionals do?A marketing research group conducting a telephone survey must contact at least 150 wives and 120 husbands. It costs P100 to make a daytime call and (because of higher labor costs) P150 to make an evening call. On average, daytime calls reach wives 30% of the time, husbands 10% of the time, and neither of these 60% of the time, whereas evening calls reach wives 30% of the time, husbands 30% of the time, and neither of these 40% of the time. Staffing considerations mean that daytime calls must be less than or equal to half of the total calls made. How many should be interviewed at each period to minimize the cost of completing the survey? fomulate the LP Model; identify the decision variables used in the model; and determine the optimal solution using graphical method.The KLM Christmas tree Farm owns a plot of land with 5000 evergreen trees.Each year KLM allows retailers of Christmas trees to select and cut trees for sale to individualcustomers. KLM protects small trees (usually less than 4 feet tall) so that they will be availablefor sale in future years. Currently, 1500 trees are classified as protected trees, while theremaining 3500 are available for cutting. However, even though a tree is available for cuttingin a given year, it may not be selected for cutting until future years. Most trees not cut in agiven year live until the next year, but some diseased trees are lost every year. In viewing the KLM Christmas tree operation as a Markov process with yearly periods, we define thefollowing four states:
- Two of the mathematics professors at Enormous State University are Professor A (known for easy grading) and Professor F (known for tough grading). Last semester, roughly three-fifths of Professor F's class consisted of former students of Professor A; these students apparently felt encouraged by their (utterly undeserved) high grades. (Professor F's own former students had fled in droves to Professor A's class to try to shore up their grade point averages.) At the end of the semester, as might have been predicted, all of Professor A's former students wound up with a C− or lower. The rest of the students in the class—former students of Professor F who had decided to "stick it out"—fared better, and one-fourth of them earned higher than a C−. After discovering what had befallen them, all the students who earned C− or lower got together and decided to send a delegation to the Department Chair to complain that their grade point averages had been ruined by this callous and heartless beast!…A national study found that treating people appropriately forhigh blood pressure reduced their overall mortality by 20%.Treating people adequately for hypertension has been difficult because it is estimated that 50% of hypertensives donot know they have high blood pressure, 50% of those whodo know are inadequately treated by their physicians, and50% who are appropriately treated fail to follow this treatment by taking the right number of pills. 2 If the preceding 50% rates were each reduced to40% by a massive education program, then what effectwould this change have on the overall mortality rate amongtrue hypertensives; that is, would the mortality rate decreaseand, if so, what percentage of deaths among hypertensivescould be prevented by the education program?The cashier line of a canteen can facilitate up to 60 customers an hour. Frequenters of thecanteen arrive at an average of 50 an hour. Suppose that management wants toevaluate the desirability of opening a second order-processing station so that twocustomers can be served simultaneously. Assume a single waiting line with the firstcustomer in line moving to the first available server.a. What is the average arrival time in minutes of customers?b. What is the average service time in minutes of the canteen?c. What is the probability that the canteen has a customer?d. What is the probability that the canteen does not have any customer?e. How long would the line be on average (average number of customers in thesystem)?f. How many people are waiting to be served on average?g. How long in minutes would it take the customer from lining up until he leaves thewaiting line?h. How long in minutes would a customer wait to be served on average?i. Find the probability that there are 7 customers in the…
- An explosion at a construction site could haveoccurred as the result of static electricity, malfunctioningof equipment, carelessness, or sabotage. Interviews withconstruction engineers analyzing the risks involved ledto the estimates that such an explosion would occur withprobability 0.25 as a result of static electricity, 0.20 as aresult of malfunctioning of equipment, 0.40 as a result ofcarelessness, and 0.75 as a result of sabotage. It is alsofelt that the prior probabilities of the four causes of theexplosion are 0.20, 0.40, 0.25, and 0.15. Based on all thisinformation, what is(a) the most likely cause of the explosion;(b) the least likely cause of the explosion?We wish to demonstrate that the average time to graduate from Tulane is affected by the students having taken AP calculus in high school. Specially, we wish to demonstrate that students who have taken AP calculus in high school graduate an average of more than 0.25 years sooner than students who have not taken AP calculus in high school. If we let denote the average time to graduate for students who have not taken AP calculus and denotes the average time to graduate for students who have taken AP calculus, then select the appropriate alternative hypothesis.Suppose insurance agency services customers who have both a homeowner’s policy and an automobile policy. For each type of policy, a deductible amount must be specified. For an automobile policy, the choices are TZS100 and TZS250, whereas for a homeowner’s policy, the choices are 0, TZS100, and TZS200. Suppose also that an individual is selected at random from the agency’s files. Let X = his deductible amount on the auto policy and Y = his deductible amount on the homeowner’s policy (a) What are the possible (X, Y) pairs? (b) Suppose the joint probability mass function is given by the insurance company in the accompanying joint probability in the following Table Table: Discrete Joint Probability Distribution for X and Y P(x,y) 0 100 200 X 100 0.2 0.10 0.2 250 0.05 0.15 0.3 What is p (100, 100) What is P (Y greater than 100)?
- The television show Lett3rs has been successful for many years. That show recently had a share of 19, which means, that among the TV sets in use, 19% were tuned to Lett3rs. An advertiser wants to verify that 19% share value by conducting its own survey, and a pilot survey begins with 10 households have TV sets in use at the time of a Lett3rs broadcast. If at most one household is tuned to Lett3rs, does it appear that the 19% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Lett3rs unusual?) A. no, it is not wrongB. yes, it is wrongThe process for cleaning up waste in a nuclear reactor core room eliminates 85% of the waste present in the area. If there is 1.7 kg of waste in the room at the beginning of the monitoring period and 2 kg of additionalwaste are generated each week, determine a recurrence relation and initial conditions describing the amount wn, of waste in the core room at the end of week n of the monitoring period.Suppose that a magazinemagazine predicted that Candidate A would defeat Candidate B in a certain election. They conducted a poll of its subscribersits subscribers with a response rate of 2424%. On the basis of the results, the magazinemagazine predicted that Candidate A would win with 57% of the popular vote. However, Candidate B won the election with about 62% of the popular vote. At the time of this poll, most subscribers to the magazinesubscribers to the magazine belonged to the party of Candidate A. Name two biases that led to this incorrect prediction.Choose the correct answer below. A.Nonresponse bias: The low response rate caused bias.Response bias: The way the poll was administered showed bias. B.Sampling bias: Using an incorrect frame led to undercoverage.Nonresponse bias: The low response rate caused bias. C.Sampling bias: Using an incorrect frame led to undercoverage.Response bias: The way the poll was administered showed bias. Click to select your answer.