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Unformatted text preview: Lesson 4 Homework Solutions 6.3 Boston Red Sox hitting : a) The probabilities give a legitimate probability distribution because each one is between 0 and 1 and the sum of all of them is 1. b) = 0P(0) + 1P(1) + 2P(2) + 3P(3) + 4P(4) = 0(0.718) + 1(0.174) + 2(0.065) + 3(0.004) + 4(0.039) =0.472 c) The mean represents a long term average number of bases for each time at bat. and therefore does not necessarily have to be a whole number 6.5 Bilingual Canadians?: a) Their corresponding probabilities are not the same; that is, each x value (0, 1, and 2) does not carry the same weight. b) =0(0.02) + 1(0.81) + 2(0.17) = 1.15 6.15 Tail probability in graph : The observation would fall 0.67 standard deviations above the mean, and thus, would have a z-score of 0.67. Looking up this z-score in Table A, we see that this corresponds to a cumulative probability of 0.749. If we subtract this from 1.0, we see that the probability that an observation falls above this point (in the shaded region) is 0.251. 6.18 z-score for given probability in tails : a) First we calculate the cumulative probability for the total probability of 0.02 in the tails. We divide 0.02 by two to determine the probability in each tail, 0.01. Then tails....
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- Spring '11