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1A.

A couple plans to have three children. There are 8 possible arrangements of girls and boys. For example, GGB means the rst two children are girls and the third child is a boy. All 8 arrangements are (approximately) equally likely. (a) Write down all 8 arrangements of the sexes of three children in alphabetical order. What is the probability of any one of these arrangements? E (b) Let X be the number of boys the couple has. What is the probability that X = 2? S (c) Starting from your work in (a), find the distribution of X. That is, what values can X take, and what are the probabilities for each value? (List the values of X in ascending order.) Xl ll ll ll l P(X)l ll ll ll l An SRS of 400 American adults is asked, "What do you think is the most serious problem facing our schools?" Suppose that in fact 45% of all adults would answer "violence" if asked this question. The proportion [3 of the sample who answer "violence\" will vary in repeated sampling. In fact, we can assign probabilities to values of [3 using the normal density curve with mean 0.45 and standard deviation 0.025. Use this density curve to find the probabilities of the following events. (a) At least 50% of the sample believes that violence is the schools' most serious problem. E (b) Less than 40% of the sample believes that Violence if the most serious problem. S (c) The sample proportion is between 0.4 and 0.5. S Choose an American household at random and let the random variable Y be the number of persons living in the household. Number of persons 1 2 3 4 5 6 7 Household probability 0.28 0.34 0.17 0.10 0.07 0.03 0.01 Family probability 0 0.42 0.23 0.21 0.09 0.03 0.02 (a) Express "more than one person lives in this household" in terms of Y. \"-Y: What is the probability of this event? S (b) What is P(2