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Quantitative Methods in Economics I 2008-11_Test2

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Department
Economics
Course
ECO220Y1
Professor
vector
Semester
Fall

Description
ECMB11H3 Sections L30 and L60 Quantitative Methods in Economics I Department of Management University of Toronto at Scarborough Fall 2008 Dr. Yu Test 2 Date: Saturday November 15, 2008 Time allowed: Two (2) hours Aids allowed: Calculator and one aid sheet (two 8.5"x11" pages) Notes: • This test consists of 23 questions in 8 pages in cluding this cover page. It is the stude nt’s responsibility to ha nd in a comple te test. Any missing page will get a zero mark. • Statistical tables (Binomial, Po isson and Standard Norm al) are provided separately. • Show your work in part 2. No m arks will be given if you do not show your work. • This test is worth 30% of your course grade. Print Last Name: Solution Given Name: Student Number: Circle your Section: L30 Wednesday 7 pm L60 Online Do not write on the space below, for markers only. Page Question Max Mark 2-4 1-18 54 5 19 5 5 20 5 6 21 10 7 22 12 8 23 14 Total 100 1 Part 1 Multiple Choice. 3 marks for each question. Select the BEST answer. No part marks. 1. A sample of size 100 is selected fr om a Poisson population with m ean 1. The distribution of the sample mean is best described as (a) Poisson with mean 1. (b) Poisson with mean 0.01. (c) Normal with mean 1 and variance 1. √ (d) Normal with mean 1 and variance 0.01 (e) Binomial with mean 1 and variance 1. 2. In a city, household incom e follows a bell shape population with a m ean of $55,000 and standard deviation of $12,000. The 99th percentile of household income in this city is closest to √ (a) $92,960 (b) $95,900 (c) $99,000 (d) $101,000 (e) $807,906 3. Random variable X follows a norm al distribution with m ean 10 a nd standard deviation 2. The probability that X is less than 5 is closest to (a) 0.00 √ (b) 0.01 (c) 0.02 (d) 0.03 (e) 0.04 4. On the average, the neg otiated selling price of a particular type of car in Toronto is $23,000. Assum e that the negotiated selling price follow a normal distribution. What is the proba bility that for a random ly selected deal, a buyer pays a price m ore than one standard deviation from t he average? √ (a) 0.1587 (b) 0.1915 (c) 0.2301 (d) 0.3413 (e) 0.4501 5. A manufacturer of a hous ehold appliance claim s that only 2% of their products need a service call for repair during the first year of ownership. A consumer protection association wants to check the claim by surveying 500 househ olds that recently purchas ed one of the manufacturer’s appliances. W hat is th e probability that m ore than 3% of the sam pled products need a service call in the first year of ownership? (a) 0.0125 (b) 0.0245 (c) 0.0372 (d) 0.0450 √(e) 0.0548 2 6. Suppose you draw a random sa mple of 100 observations from a population with mean 20 and standard deviation 5. What is the probability that the sample mean is greater than 21? (a) 0.0002 √ (b) 0.0228 (c) 0.1510 (d) 0.3166 (e) 0.4207 7. Random variable X is normally distributed with mean µ and variance µ .2 Suppose P − 4 < X < 8 = 0.9974 . The value of µ is closest to (a) 1 √ (b) 2 (c) 4 (d) 6 (e) 8 Questions 8-9 In the population, suppose 10% of the hom es have 1 bed room, 50% have 2 bedroom s and 40% have 3 bedroom s. Consider a survey that as ks whether a respondent’s home has 1, 2 or 3 bedrooms. Assume that survey responses are independent. 8. After speaking with 3 respondents, what is the probability that you receive three d ifferent answers : one lives in a 1 bedroom , one lives in a 2 bedroom, and one lives in a 3 bedroom? (a) 0.08 (b) 0.10 √ (c) 0.12 (d) 0.54 (e) 0.66 9. After speaking with 300 respondents, wh at is the probability that m ore than 40% live in homes with 3 bedrooms? (a) 0.30 (b) 0.33 (c) 0.35 (d) 0.40 √ (e) 0.50 Questions 10-13 Suppose random variable X has the probability distribution X 0 1.5 2 P(X) 0.2 0.2 0.6 10. The average of X is closest to (a) 0.5 (b) 0.75 √ (c) 1.5 (d) 1.75 (e) 1.95 11. The variance of X is closest to (a) 0.2 (b) 0.3 (c) 0.4 (d) 0.5 √ (e) 0.6 3 12. A random sam ple of s ize 100 is sele cted from this distribution. The average of the sample mean is closest to (a) 0.5 (b) 0.75 √ (c) 1.5 (d) 1.75 (e) 1.95 13. A random sam ple of s ize 100 is sele cted from this distribution. The standard deviation of the sample mean is closest to (a) 0.0175 (b) 0.0355 (c) 0.0575 (d) 0.0705 √ (e) 0.0775 Question 14-18 The annual bonus of employees is nor mally distributed with a m ean of $1000 and a standard deviation of $200. 14. A randomly selected employee receives less than half of the annual bonus is closest to √ (a) 0.0062 (b) 0.1336 (c) 0.2574 (d) 0.4332 (e) 0.8664 15. A random ly selected em ployee receives an annual bon us within 1 .5 standard deviations from the average is closest to (a) 0.0668 (b) 0.1336 (c) 0.2574 (d) 0.4332 √ (e) 0.8664 16. Four employees are selected at ran dom. The probability th at only one of them receives an annual bonus of less than $800 is closest to (a) 0.1585 (b) 0.25 (c) 0.275 √ (d) 0.378 (e) 0.8413 17. Four hundred em ployees are selected at rand om. The probability that more than 220 of them receive annual bon us of m ore than $100 0 is approximately between √ (a) 0.0228 and 0.0256 (b) 0.1352 and 0.1753 (c) 0.2518 and 0.3528 (d) 0.3712 and 0.3912 (e) 0.4122 and 0.5121 18 Four hundred employees are selected at random. The probability that their average annual bonus is over $980 is closest to (a) 0.0228 (b) 0.2557 (c) 0.4886 (d) 0.7329 √ (e) 0.9772 4 Part 2 Show your work in each question. 19. (5 marks) On the average a grocer sells 3 of a certain article per
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