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East West Distributing is in the process of trying to determine where they should schedule next year's production of a popular line of kitchen utensils that they distribute. Manufacturers in four different countries have submitted bids to East West. However, a pending trade bill in Congress will greatly affect the cost to East West due to proposed tariffs, favorable trading status, etc.A manufacturing company is considering expanding its production capacity to meet a growing demand for its product line of air fresheners. The alternatives are to build a new plant, expand the old plant, or do nothing. The marketing department estimates a 35 percent probability of a market upturn, a 40 percent probability of a stable market, and a 25 percent probability of a market downturn. Georgia Swain, the firm's capital appropriations analyst, estimates the following annual returns for these alternatives:A calculus instructor uses computer aided instruction and allows students to take the midterm exam as many times as needed until a passing grade is obtained. Following is a record of the number of students in a class of 20 who took the test each number of times.After careful analysis, East West has determined the following cost breakdown for the four manufacturers (in $1,000's) based on whether or not the trade bill passes:Bill PassesBill FailsCountry A260210Country B320160Country C240240Country D275210a.If East West estimates that there is a 40% chance of the bill passing, which country should they choose for manufacturing?b.Over what range of values for the "bill passing" will the solution in part (a) remain optimal?MarketUpturnStableMarketMarketDownturnBuild new plant$690,000$(130,000)$(150,000)Expand old plant 490,000 (45,000) (65,000)Do nothing 50,000 0 (20,000)a. What should the company do?b. What returns will accrue to the company if your recommendation is followed?(I created the table below). Decision tree:StudentsNumber of Tests101 72 23 14a.Use the relative frequency approach to construct a probability distribution and show that it satisfies the required condition.b.Find the expected value of the number of tests taken.c.Compute the variance.d.Compute the standard deviation.