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Shoes How many pairs of shoes do students have? Do girls have more shoes than boys? Here are data from a random sample of 20 female and 20 male students at a large high school: $$ \begin{array}{llrrrrrrrrr} \hline \text { Female: } & 50 & 26 & 26 & 31 & 57 & 19 & 24 & 22 & 23 & 38 \\ & 13 & 50 & 13 & 34 & 23 & 30 & 49 & 13 & 15 & 51 \\ \text { Male: } & 14 & 7 & 6 & 5 & 12 & 38 & 8 & 7 & 10 & 10 \\ & 10 & 11 & 4 & 5 & 22 & 7 & 5 & 10 & 35 & 7 \\ \hline \end{array} $$ (a) Find and interpret the percentile in the female distribution for the girl with 22 pairs of shoes. (b) Find and interpret the percentile in the male distribution for the boy with 22 pairs of shoes. (c) Who is more unusual: the girl with 22 pairs of shoes or the boy with 22 pairs of shoes? Explain.

Eleanor scores 680 on the SAT Mathematics test. The distribution of SAT scores is symmetric and single-peaked, with mean 500 and standard deviation 100 . Gerald takes the American College Testing (ACT) Mathematics test and scores 27. ACT scores also follow a symmetric, single-peaked distribution-but with mean 18 and standard deviation \(6 .\) Find the standardized scores for both students. Assuming that both tests measure the same kind of ability, who has the higher score?

George has an average bowling score of 180 and bowls in a league where the average for all bowlers is 150 and the standard deviation is \(20 .\) Bill has an average bowling score of 190 and bowls in a league where the average is 160 and the standard deviation is \(15 .\) Who ranks higher in his own league, George or Bill? (a) Bill, because his 190 is higher than George's 180 . (b) Bill, because his standardized score is higher than George's. (c) Bill and George have the same rank in their leagues, because both are 30 pins above the mean. (d) George, because his standardized score is higher than Bill's. (e) George, because the standard deviation of bowling scores is higher in his league.

Deciles The deciles of any distribution are the values at the 10 th, \(20 t h, \ldots, 90\) th percentiles. The first and last deciles are the l0th and the 90 th percentiles, respectively. (a) What are the first and last deciles of the standard Normal distribution? (b) The heights of young women are approximately Normal with mean 64.5 inches and standard deviation 2.5 inches. What are the first and last deciles of this distribution? Show your work.

Weights aren't Normal The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. Weights, on the other hand, are not Normally distributed. The weights of women aged 20 to 29 have mean 141.7 pounds and median 133.2 pounds. The first and third quartiles are 118.3 pounds and 157.3 pounds. What can you say about the shape of the weight distribution? Why?