ARE106SU09MT1KEY

# ARE106SU09MT1KEY - Name_KEY Last 4 digits of your Student...

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Name:____KEY_________________ Last 4 digits of your Student ID Number:__________ Managerial Economics (ARE) 106 University of California, Davis, Summer Session II, 2009 Dr. John H. Constantine Midterm 1, Thursday, August 13, 2009 75 TOTAL POINTS

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1 Problem 1 (25 points; 5 points for each part) : Joe, a building contractor, claims he can renovate a 200-square foot kitchen and dining room in 40 work hours, on average, with a standard deviation of 5 hours ( μ = 40; σ = 5). Given his past history of renovating buildings, Joe assumes that similar projects are normally distributed with the mean and standard deviation as noted above. (a) What is the likelihood that a given project will be completed in less than 35 hours? 1 5 40 35 x z = = σ μ = P(x < 35) = P(z < – 1.00) = 1 – 0.3413 = 0.1587 = 15.87% (b) What is the likelihood that a given project will be completed in between 28 and 32 hours? 4 . 2 5 40 28 x z L = = σ μ = ; 6 . 1 5 40 32 z H = = P(28 < x < 32) = P(– 2.4 < z < – 1.6) = 0.4918 – 0.4452 = 0.0466 = 4.66% (c) What is the likelihood that a given project will be completed in between 38 and 50 hours? 4 . 0 5 40 38 x z L = = σ μ = ; 00 . 2 5 40 50 z H = = P(38 < x < 50) = P(–0.4 < z < 50) = ??? (d) We would expect that 10% of such projects will require more than how many hours? At 10% probability, z = 1.255 5 40 x 255 . 1 = ; x = 46.275 hours. (e) Calculate the lower and upper bounds for the random variable which contains the middle 50%” of such projects (that is, those that fall within quartiles 2 and 3). The term “quartile” is used on Homework 1 .
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## This note was uploaded on 11/19/2009 for the course ARE ARE106 taught by Professor Constantine during the Spring '09 term at UC Davis.

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ARE106SU09MT1KEY - Name_KEY Last 4 digits of your Student...

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