Height and Weight Distribution The chart shown on the

Chapter 13, Problem 13.1.179

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Height and Weight Distribution The chart shown on the right uses the symbol s to represent the standard deviation. Note that 2s represents the value that is two standard deviations above the mean; -2s represents the value that is two standard deviations below the mean. The unshaded areas, from two standard deviations below the mean to two standard deviations above the mean, are considered the normal range. For example, the average (mean) 8-yearold boy has a height of about 50 inches, but any heights between approximately 45 inches and 55 inches are considered normal for 8-year-old boys. Refer to the chart below to answer the following questions. Inches Pounds Kilogram Centimeters Boys physical development, 118 years *Supine length to 6 years, standing height from 6 to 18 years Height Weight * 75 65 55 45 35 25 15 180 180 200 160 140 120 100 80 60 40 20 160 140 120 100 80 60 40 +2 mean mean 2 2 +2 85 75 65 55 45 35 25 15 5 Age in years 1 18 3 5 7 9 11 13 15 17 a) What happens to the standard deviation for weights of boys as the age of boys increases? What is the significance of this fact? b) At age 16, what is the mean weight, in pounds, of boys? c) What is the approximate standard deviation of boys weights at age 16? d) Determine the mean weight and normal range for boys at age 13. e) Determine the mean height and normal range for boys at age 13. f ) Assuming that this chart was constructed so that approximately 95% of all boys are always in the normal range, determine what percentage of boys are not in the normal range

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