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Section 7.2 Sampling Distribution of the Sample Mean Statistics Problems from 437 to 439 of text. P7.) The distribution of the population of the number of motor vehicles per household and sampling distributions of the mean for samples of size 4 and 10 are shown in Display 7.28 on page 437. a.) Which distribution is which? b.) The mean of the population is about 1.7. Theoretically, what is the mean of the sampling distribution for samples of size: 4? 10? c.) The standard deviation of the population is about 1. Theoretically, what is the SE of the sampling distribution for samples of size 4? size 10? P8.) From 1910 through 1919, the single-season batting averages of individual Major League Baseball players had a distribution that was approximately normal, with mean 0.266 and standard deviation 0.037. Suppose you construct the sampling distribution of the mean batting average for random samples of 15 players. What are the shape, mean, and standard error of this distribution? Shape is: Mean is: Standard error is: P9.) Refer to the table below. Suppose a television network selects a random sample of 1000 families in the US for a survey on TV viewing habits. Number of Children 0 1 2 3 4 (or more) TOTAL Number of Families 53 20 17 7 3 100 a.) Describe the distribution of the possible values of the average number of children per family. b.) What average numbers of children are reasonably likely? c.) What is the probability that the average number of children per family will be 0.8 or less? P10.) Last January 1, Jenny thought about buying individual stocks. Over the next year, the mean of the percentage increases in individual stock prices is 6.5% and the standard deviation of these percentage increases is 12.8%. The distribution of price increases is approximately normal. a.) If Jenny had picked one stock at random, what is the probability that it would have gone down in price? b.) If Jenny had picked four stocks at random, what is the probability that their mean percentage increase would be negative? c.) If Jenny had picked eight stocks at random, what is the probability that their mean percentage increase would be between 8% and 10%? d.) If Jenny had picked eight stocks at random, what mean percentage changes in price are reasonably likely? (In other words, find the interval that contains the middle 95% of possible mean percentage increases in value.) P13.) The distribution of the number of motor vehicles per household in the US is roughly symmetric, with mean 1.7 and standard deviation 1.0. a.) If you pick 15 households at random, what is the probability that they have at least 30 motor vehicles among them? b.) If you pick 20 households at random, what is the probability that they have between 25 and 30 motor vehicles among them? P14.) Refer to the table below. Suppose a television network selects a random sample of 1000 families in the US for a survey on TV viewing habits. Number of Children 0 1 2 3 4 (or more) TOTAL Number of Families 53 20 17 7 3 100 a.) Do you think it is reasonably likely that a sample of 1000 households will produce at least 1000 children? Explain you reasoning. b.) If the network changes to a random sample of 1200 households, does this dramatically improve the chances of seeing at least 1000 children in the sampled households? Explain.