# PS3solution - San Francisco State University Department of...

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Unformatted text preview: San Francisco State University Department of Economics Econ 311 / Fall 2008 Professor: Sang-Yeob Lee Econ 311: Problem Set #3 Suggested Answers Q.1 The number of computers sold per day at Dan’s Computer works is defined by the following prob- ability distribution: X 1 2 3 4 5 6 P(x) 0.05 0.10 0.20 0.20 0.20 0.15 0.10 a P ( 3 ≤ x < 6 ) ? P ( 3 ≤ x < 6 ) = P ( 3 ) + P ( 4 ) + P ( 5 ) = 0.20 + 0.20 + 0.15 = 0.55 b P ( x > 3 ) ? P ( x > 3 ) = P ( 4 ) + P ( 5 ) + P ( 6 ) = 0.20 + 0.15 + 0.10 = 0.45 c P ( x ≤ 4 ) ? P ( x ≤ 4 ) = P ( 1 ) + P ( 2 ) + P ( 3 ) + P ( 4 ) = 1- ( P ( 5 ) + P ( 6 )) = 1- 0.15- 0.10 = 0.75 d P ( 2 < x ≤ 5 ) ? P ( 2 < x ≤ 5 ) = P ( 3 ) + P ( 4 ) + P ( 5 ) = 0.55 Q.2 A corporation produces packages of paper clips. The number of clips packages varies, as indicated in the accompanying table. Number of clips 47 48 49 50 51 52 53 Proportion of packages 0.04 0.13 0.21 0.29 0.20 0.10 0.03 Cumulative prob. 0.04 0.17 0.38 0.67 0.87 0.97 1.00 a Draw the probability function. b Calculate and draw the cumulative probability function. c What is the probability that a randomly chosen package will contain between 49 and 51 clips (inclu- sive)? P ( 49 ≥ X ≤ 51 ) = P ( 49 ) + P ( 50 ) + P ( 51 ) = 0.70. d Two packages are chosen at random. What is the probability that at least one of them contains at least 50 clips?...
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PS3solution - San Francisco State University Department of...

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