HW 4 Solutions

HW 4 Solutions - Spring 2007 BA 240 W. Li Homework 4...

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Spring 2007 BA 240 W. Li Homework 4 Solution 1 Homework 4 Solution Problem 4.15: a) The simple events are (where H = head, T = tail): HHH HHT HTH THH HTT THT TTH TTT x = # of heads 3 2 2 2 1 1 1 0 b) If each event is equally likely, then p (each simple event) = 1/ n = 1/8 p (3) = 1/8 p (2) = 1/8 + 1/8 + 1/8 = 3/8 p (1) = 1/8 + 1/8 + 1/8 = 3/8 p (0) = 1/8 c) Histogram of Flip Coin 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0123 x (# of Heads) p(x) d) p ( x = 2 or x = 3) = p (2) + p (3) = 3/8 + 1/8 = 4/8 = 1/2 Problem 4.36: a) = + + + + = + + + + = = 8 . 1 16 / 6 . 74 . 3 . 0 ) 04 (. 4 ) 20 (. 3 ) 37 (. 2 ) 30 (. 1 ) 09 (. 0 ) ( ) ( x p x x E In a random samples of 4 homes, the average number of homes with high dust mite levels is 1.8. b) 98 . 1936 . 2880 . 0148 . 1920 . 2916 . ) 04 (. ) 8 . 1 4 ( ) 2 (. ) 8 . 1 3 ( ) 37 (. ) 8 . 1 2 ( ) 3 (. ) 8 . 1 1 ( ) 09 (. ) 8 . 1 0 ( ) ( ) ( 2 2 2 2 2 2 2 = + + + + = + + + + = = x p x µ σ 9899 . 98 . = =
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Spring 2007 BA 240 W. Li Homework 4 Solution 2 c) ) 7798 . 3 , 1798 . ( 9798 . 1 8 . 1 2 ± ± σ µ 96 . 20 . 37 . 30 . 09 . ) 3 ( ) 2 ( ) 1 ( ) 0 ( ) 7798 . 3 1798 . ( = + + + = + + + = < < p p p p x p Chebyshev’s Theorem says that the interval 2 ± will contain at least 75% (.75) of data. The Empirical Rule says that approximately 95.44% (.9544) of the data will be contained in the interval. Both Chebyshev’s Theorem and the Empirical Rule fit the distribution. Problem 4.40: Let x = winnings in the Florida lottery. The probability distribution for x is: X p(x) -$1 22,999,999 / 23,000,000
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HW 4 Solutions - Spring 2007 BA 240 W. Li Homework 4...

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