hw2_answer_su05

hw2_answer_su05 - Economics 120A Professor Yongil Jeon...

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Economics 120A Name: _________________________ Professor Yongil Jeon Summer 2005 Student ID#: _________________________ Answer to Homework #2 (Final Exam, Summer 2004) 1. (10 points) Given that z is a standard normal random variable, compute the following probabilities (a) (3 points) P(-1.98 z 0.49) (b) (3 points) P(0.52 z 1.22) (c) (4 points) P(-1.75 z -1.04) . di norm(1.98) .9761 . di norm(0.49) .6879 . di norm(0.52) .6985 . di norm(1.22) .8888 . di norm(1.75) .9599 . di norm(1.04) .8508 (Answer) (a) P(-1.98 z 0.49) = F(0.49)-F(-1.98)= F(0.49)-[1-F(1.98)] = 0.6879 – (1-0.9761) = 0.6640 (b) P(0.52 z 1.22) = F(1.22)-F(0.52)=0.8888-0.6985=0.1903 (c) P(-1.75 z -1.04)=F(-1.04)-F(-1.75)= [1-F(1.04)]-[1-F(1.75)]=(1-0.8508)-(1-0.9599)= 0.1091
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2 Answer to HW #2, ECON 120A, Summer 2004 2. (10 points) The average time a subscriber spends reading The Wall Street Journal is 49 minutes. Assume the standard deviation is 16 minutes and that the times are normally distributed (a) (3 points) What is the probability a subscriber will spend at least 1 hour reading the Journal ? (b) (3 points) What is the probability a subscriber will spend no more than 30 minutes reading the Journal ? (c) (4 points) For the 10% who spend the most time reading the Journal , how much time do they spend? That is, find z-score so that P( Z z-score) = 0.10. . di norm(0.69) .7549 . di norm(1.19) .8830 . di norm(1.28) .9000 (Answer) (a) P( X 60) = P 16 49 60 16 49 X = P ( ) 69 . 0 Z =1-F(0.69)=1-0.7549=0.2451. (b) ( X 30) = P 16 49 30 16 49 X = P ( ) 19 . 1 Z =1-F(1.19)=1-0.8830=0.1170. (c) A z-score of 1.28 cuts off 10% in upper tail: now, solve for corresponding value of x 1.28= 16 49 X X=49+16*1.28=69.48 So, 10% of subscribers spend 69.48 minutes or more reading The Wall Street Journal .
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3 Answer to HW #2, ECON 120A, Summer 2004 3. (15 points) A population has a mean of 200 and a standard deviation of 50. A random sample of size 100 will be taken and the sample mean x will be used to estimate the population
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This note was uploaded on 04/15/2008 for the course ECON 120A taught by Professor Jeyeon during the Summer '08 term at UCSD.

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hw2_answer_su05 - Economics 120A Professor Yongil Jeon...

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