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# Hw2Sol - SIEO 3600(IEOR Majors Introduction to Probability...

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SIEO 3600 (IEOR Majors) Assignment #2 Introduction to Probability and Statistics February 2, 2010 Assignment #2 – due February 2nd, 2010 1. The following are the grade point averages of 30 students recently admitted to the gradu- ate program in the Department of Industrial Engineering and Operations Research at the University of California at Berkeley. 3 . 46 , 3 . 72 , 3 . 95 , 3 . 55 , 3 . 62 , 3 . 80 , 3 . 86 , 3 . 71 , 3 . 56 , 3 . 49 , 3 . 96 , 3 . 90 , 3 . 70 , 3 . 61 , 3 . 72 , 3 . 65 , 3 . 48 , 3 . 87 , 3 . 82 , 3 . 91 , 3 . 69 , 3 . 67 , 3 . 72 , 3 . 66 , 3 . 79 , 3 . 75 , 3 . 93 , 3 . 74 , 3 . 50 , 3 . 83 (a) Represent the preceding data in a stem and leaf plot. (b) Calculate the sample mean x ( n ). (c) Calculate the sample standard deviation s ( n ). (d) Determine the proportion of the data values that lies within x ( n ) ± 1 . 5 s ( n ) and compare with the lower bound given by Chebyshev’s inequality. Solution: (a) Omitted (b) ¯ x ( n ) = 3 . 721 (c) S x ( n ) = 0 . 1457 (d) Chebyshev’s inequality says that | S 1 . 5 | n = S 1 . 5 30 5 9 , i.e., | S 1 . 5 | ≥ 17. By simply counting, we have | S 1 . 5 | = 24, which satisfies the inequality. 2. Let S = { 1 , 2 , 3 , 4 , 5 , 6 , 7 } , E = { 1 , 3 , 5 , 7 } , F = { 7 , 4 , 6 } , G = { 1 , 4 } . Find (a) E F (b) E ( F G ) (c) E G c (d) ( E F c ) G (e) E c ( F G ) (f) ( E G ) ( F G ) Solution: (a) { 7 } (b) { 1 , 3 , 4 , 5 , 7 } (c) { 3 , 5 , 7 } (d) { 1

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Hw2Sol - SIEO 3600(IEOR Majors Introduction to Probability...

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