Mathematics for Business Decisions, Part IIHomework 10Mathematics for Business Decisions, Part IIHomework 10forMath 115b, Section: Instructor: James BarrettDate: byTeam: We, the undersigned, maintain that each of us participated fully and equally in the completion of this assignment and that the work contained herein is original. Furthermore, we acknowledge that sanctions will be imposed jointly if any part of this work is found to violate the Student Code of Conduct, the Code of Academic Integrity, or the policies and procedures established for this course. _ Name Typed Signature % of Grade__________________ ______________________________ ______________________________ ______________________________ ______________________________ ______________________________ ______________________________ _____________________________ _______________________________ _____________________________ ____________1. (i) Simulate a fixed random sample of size 1,000 from a normal random variable, T, with a mean of $3,000,000 and a standard deviation of $450,000. (ii) Compute the mean and standard deviation of your sample. (iii) Find the minimum and maximum values in your sample, and compute the range of the data in the sample.Solution. 2. Let T be the random variable from problem 1. Simulate changeable random samples of size 1,000. Arrange the Excel sheet so that it automatically computes the mean, standard, deviation, minimum, maximum, and range of each sample.Solution. 3. Let Plan C be the same as Plan B for the administrator’s salary in the text example, except that both the largest and the smallest salaries are removed from each sample of size 5 before the remaining 3 salaries are averaged. Modify Simulation in Salary.xlsx so that it estimates the expected value of the administrator’s new salary under Plan C. How much better off would the administrator be under Plan C than under Plan A?Solution. 4. Let Plan D be the same as Plan A for the administrator’s salary, except that a random sampleof 8 administrators salaries will be taken. Modify Simulation in Salary.xlsx so that it estimates the expected value of the administrator’s new salary under Plan D. Would the administrator be better or worse off under Plan D than under Plan A?Solution5. Let Y be a normal random variable with μY=100 and σY=5. (i) Use Random Number Generation to generate a set of 500 random samples, each of size 50, from Y and (ii) have Excel compute the 90% confidence interval for each sample. (iii) What fraction of the intervals contain 100, the mean of Y?Solution. 6. Let C and B be random variables for your team’s data which are analogous to those for the Class Project, as described in the Focus pages of this section. (i) Use your team’s data andnormal simulation to estimate E(C ) and E( B). Compute your company’s best signal adjustment under the assumptions that (ii) all other companies adjust by removing both the winner’s curse and blessing, and (iii) all other companies adjust by removing only the winner’s curse. Show your work, including plots of the data points for various responses, and the use of Solver to compute the best strategies. (Do not use Auction Equilibrium.xlsm for Parts (ii) and (iii).) (iv) Experiment with Auction Equilibrium.xlsm to determine a stable Nash equilibrium bidding strategy for your team’s
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