ECON 3400 Final Exam 2015

| December 12, 2017

ECON 3400Final Exam1. Probability(15 Points)Of the cars on a used car lot, 80% have air conditioning (AC) and 50% have a GPS. 30% of thecars have both.a. Fill the following contingency table. (5 points)ACGPSNo ACTotal0. GPSTotalb. What is the probability that a car has a GPS, given that it has AC?i.e., we want to find P (GPS | AC) (5 points)c. What is the probability that a car has either a GPS or AC?i.e., we want to find P (GPS AC) (5 points)2. Discrete Probability Distribution (20 Points)The J.R. Ryland Computer Company is considering a plant expansion to enable the companyto begin production of a new computer product. The companys president must determinewhether to make the expansion a medium- or large- scale project. Demand for the newproduct is uncertain, which for planning purposes may be low demand, medium demand, orhigh demand. The probability estimates for demand are .20, .50, and .30, respectively. Lettingx and y indicate the annual profit in thousands of dollars, the firms planners developed thefollowing profit forecasts for the medium- and large- scale expansion projects.DemandMedium-ScaleExpansion Profit(x)50Large-ScaleExpansion Profit(y)0Medium 0.50150100High200300LowProbability ofDemandP(i), i:{x,y}0.200.30a. Compute the expected value for the profit associated with the two expansion alternatives.Which decision is preferred for the objective of maximizing the expected profit? (10points)b. Compute the variance for the profit associate with two expansion alternatives. Whichdecision is preferred for the objective of minimizing the risk of uncertainty? (10 points)23. Binomial Probability Distribution (15 Points)The Center for Medicare and Medical Services reported that there were 295,000 appeals forhospitalization and other Part A Medicare service. For this group, 40% of first-round appealswere successful (The Wall Street Journal, October 22, 2012). Suppose 10 first-round appealshave just been received by a Medicare appeal office.a. Compute the probability that none of the appeals will be successful. (5 points)b. Compute the probability that exactly one of the appeals will be successful. (5 points)c. What is the probability that more than half of the appeals will be successful?(5 points)4. (4 Points * 5 = 20 Points)I.II.III.IV.4V.5. (5 Points * 6 = 30 Points)

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