allu tlllllltuft Willth llote unusual a quantitative SA scor

allu tlllllltuft, Willth llote unusual. a quantitative SA score of 750 or an ACT score of 28? Show your work. 3.28 Children\'s Heights Mrs. Diaz has two children: a three- year-old boy 43 inches tall and a ten-year-old girl 57 inches tall Three-year-old boys have a mean height of 38 inches and a standard deviation of 2 inches, and ten-year-old girls have a mean height of 54.5 inches and a standard deviation of 2.5 inches. Assume the dis- tributions of boys\' and girls\' heights are unimodal and symmetric. Which of Mrs. Diaz\'s children is more unusually tall for his or her age and gender? Explain, showing any calculations you perform (Source: www.kidsgrowth.com)

Solution

three year old boys

Mean = 38; stdev = 2

So the child who is 43 inches tall is more than 2 deviations from the normal mean

38 + 2(x) = 43

x = 2.5 deviations

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ten year old girls

Mean = 54.5; stdev = 2.5

So the child who is 57 inches tall is 1 deviation from the normal mean

54.5 + 2.5(x) = 57

x = 1 deviation

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Hence the three year old is unusually tall