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Mgt. 201BHomework 3 (110 points total)Due on Friday 11-10-171. (37 points) Monte Carlo Simulation.Choose your own simple problem and conduct aMonte Carlo simulation using Excel. IT IS OK TO DO (just) THIS PROBLEM 1 WITH AGROUP. EACH PERSON SHOULD PUT THE ANSWER INTO HIS/HER INDIVIDUALHOMEWORK, AND SHOULD LIST WHO THIS ONE PROBLEM WAS DONE WITH.SolutionIn this problem we sought to use Monte Carlo simulation to simulate sales for company XYZwhich sells fast moving goods (FMGs).The sales are simulated to range between $50,000 and $100,000. The graphical as well as tabularrepresentation of the summary data is given below;1

Table on Summary StatisticsMeasureValueStandard deviation14.6147Mean73.92Median72.5Mode602. (18points total)A particular type of printer ribbon is produced by only three companies,Alamo Ribbon Company, Savin Corporation and South Jersey Products. Suppose that Alamoproduces 50% of the ribbons, Savin produces 30% and South Jersey produces 20%. Accordingto a quality inspection report, 8% of the ribbons produced by Alamo are defective, 10% of theribbons produced by Savin are defective and 12% of South Jersey ribbons are defective.2A.(4 points)Assume 1,000 ribbons in the market are to be inspected. Fill in the following rawdata table:InspectedRibbonsAlamoSavinSouthJerseyDefective40302494Acceptable4602701769065003002001,000Ribbons2B. (2 points)For parts B through F use the raw data table, a probability tree or Bayes’Theorem.You may leave all answers in unreduced fractions.Not required:Ifyou explain how you get your answer in each case, either in words or by writingdown calculations, this will be used to award partial credit if you do not have the correctnumerical answer.Find the probability that a defective ribbon had been produced by Savin.Solution2

P(DefectiveproducedbySavin)=301000=0.032C. (3 points)Find the probability that a ribbon is acceptable given that it was produced bySouth Jersey.SolutionProbability(Acceptableribbon∧¿SouthJersey)=1761000=0.176Probability(ProducedbySouthJersey)=2001000=0.2Probability(Ribbonacceptable∨SouthJersey)=0.1760.2=0.882D. (3 points)Find the probability that an acceptable ribbon had been produced by Alamo.SolutionProbability(Acceptableribbon∧¿Alamo)=4601000=0.460Probability(ProducedbyAlamo)=5001000=0.5Probability(Ribbonacceptable∨Alamo)=0.4600.50=0.922E. (3 points)Find the probability that a ribbon will be defective if it is produced by Savin.SolutionProbability(Defectiveribbon∧¿Savin)=301000=0.03Probability(ProducedbySavin)=3001000=0.3Probability(Ribbonacceptable∨Alamo)=0.030.3=0.102F. (3 points)What is the posterior (i.e., updated) probability that a ribbon was produced bySouth Jersey given it is acceptable?SolutionProbability(SouthJersey∨Acceptable)=P(S|A)=P(S)P(A∨S)A3

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