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Iris Wu

ECMB11H3 Quantitative Methods in Economics I Sections L01L30 Summer 2011 Department of Management University of Toronto at Scarborough Dr Yu Final ExaminationDate Saturday August 13 2011Time allowedTwo 2 hoursAids allowedCalculator and two aid sheets four 85x11 pagesNotesThis exam consists of 22 questions in 12 pages including this cover pageIt is the students responsibility to hand in a complete testAny missing page will get a zero markStatistical tables Z t are provided separatelyShow your work in part 2No marks will be given if you do not show your workThis exam is worth 40 of your course gradePrint Last Name SolutionGiven NameStudent NumberSection circle one L01 Tuesday 9am L30 Tuesday 7pm Defer ExamPage QuestionMaxMark 26 117 517 18 78 19 109 20 1010 21 101112 22 12 Total 100 1 Part 1 Multiple Choice 3 marks for each question Circle the BEST answer No part marks1 The capacity of an office building elevator is 8 persons or 640 kg Assume that the weights of the office workers are normally distributed with mean equal to 75 kg and standard deviation equal to 9 kg What is the probability that the total weight of 8 randomly selected office workers exceeds the capacity of an elevatora 00010 b 00582 c 02912 d 07088 e 09418 881Solution 8080640XPXPXP ii811iiX7580ZPP05820571n89 2 A random sample of 100 observations is to be drawn from a population with mean 40 and standard deviation 25 The probability that the mean of the sample will exceed 45 isa 04772 b 04207 c 00793d 00228e Not possible to compute based on the information provided 4045XSolution 45XP 022802ZPP 10025n3 A random variable Y has the following probability distribution1 0 1 2 Y PY 3C 2C 04 01 The value of the constant C is a 010 b 015 c 020 d 025 e 075Solution 3C2C04011 C014 The mean life of a particular brand of light bulb is 1000 hours and the standard deviation is 50 hours We can conclude that at least 75 bulbs of this brand will last betweena 9001100 hoursb 9501050 hours c 8501150 hours d 8001200 hourse 10501250 hours 11175 using Chebyshevs rule with Solution 12k at least 75 242900502100011005021000 andbulbs will last between2
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