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7.14 According to government data, 22% of American novel aimed at teenagers, the mean word length is children under the age of 6 live in households with 4.3 letters with a standard deviation of 2.5 letters. incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of Both distributions of word length are unimodal and 300 children from one state and finds that p = 0.29 skewed to the right. Independent random samples of 35 words are selected from each book. Let Xc repre- Find the probability that at least 29% of the sample sent the sample mean word length in the children's are from poverty-level households, assuming that 22% book and let IT represent the sample mean word of all children under the age of 6 in this state live in length in the teen novel. poverty-level households. (a) Find the mean of the sampling distribution of XC - TT. (b) Based on your answer to part (a), is there convincing evidence that the percentage of children under the b) Calculate and interpret the standard deviation of the age of 6 living in households with incomes less than sampling distribution. Verify that the 10% condition is met. the official poverty level in this state is greater than the (c) Justify that the shape of the sampling distribution is national value of 22%? Explain your reasoning. approximately Normal. 17.15 In a children's book, the mean word length is 3.7 d) What is the probability that the sample mean word letters with a standard deviation of 2. 1 letters. In a length is greater in the sample from the children's book than in the sample from the teen novel? Cumulative Ap Practice Test 2 Section 1: Multiple Choice Choose the best answer for each question. AP2.1 The five-number summary for a data set is given by AP2.3 In a certain large population of adults, the distribu- min = 5, 91 = 18, median = 20, Q3 = 40, max = 75. tion of IQ scores is strongly left-skewed with a mean If you wanted to construct a boxplot for the data set of 122 and a standard deviation of 5. Suppose 200 that would show outliers, if any existed, what would adults are randomly selected from this population be the maximum possible length of the right-side for a market research study. For SRSs of size 200, the "whisker"? listribution of sample mean IQ score is (a) 33 (a) left-skewed with mean 122 and standard deviation 0.35. ( 6) 35 (b) exactly Normal with mean 122 and standard deviation 5. ( C) 45 (c ) exactly Normal with mean 122 and standard deviation ( d) 53 0.35. (e) 55 (d) approximately Normal with mean 122 and standard deviation 5. AP2.2 The probability distribution for the number of heads (e) approximately Normal with mean 122 and standard in four tosses of a coin is given by deviation 0.35. AP2.4 A 10-question multiple-choice exam offers 5 choices Number of heads 0 1 2 3 for each question. Jason just guesses the answers, so Probability 0.0625 0.2500 0.3750 0.2500 0.0625 he has probability 1/5 of getting any one answer cor- rect. You want to perform a simulation to determine The probability of getting at least one tail in four tosses of a the number of correct answers that Jason gets. What coin is would be a proper way to use a table of random dig- (a) 0.2500. its to do this? (b) 0.3125. (a) One digit from the random digit table simulates one C) 0.6875 answer, with 5 = correct and all other digits = incorrect. Ten digits from the table simulate 10 answers. (d) 0.9375. (b) One digit from the random digit table simulates one (e) 0.0625 answer, with 0 or 1 = correct and all other