To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by50foot squares, and counted the number of trees with

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To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by50foot squares, and counted the number of trees with diameters exceeding 12 inches in each square. The data are listed here. (a) Construct a relative frequency histogram to describe the data. Frequency 0f lumber Frequency of lumber Frequency of lumber 0.40 0.40 0.40 E 0.35 E' 0.35 E' 0.35 g 0.30 g 0.30 g 0.30 E 0.25 5' 0.25 E 0.25 a a 1-4 H 0.20 H 0.20 H 0.20 e e a: .5 0.15 .5 0.15 .3 0.15 e: 0.10 a: 0.10 a 0.10 m 0.05 g 0.05 m 0.05 llli llli ii 01234567391011121314 01234557391011121314 01234507391011121514 amount of lumber amount of lumber amount of lumber @ Q 0 Frequency of lumber 0.40 E' 0.35 5 030 g . .4 0.25 a H 0.20 a: .g 0.15 m a 0.10 \"4 0.05 my m 01234567891011121314 amount of lumber @ (b) Calculate the sample mean 7! as an estimate of a, the mean number of trees for all 50-by50foot squares in the tract. (Round your answer to three decimal places.) x = 7.557 timber trees (c) Calculate s for the data. (Round your answer to three decimal places.) s = 2.204 timber trees Construct the intervals ,Q i s, E e 25, and J? a: 35. Calculate the percentage of squares falling into each of the three intervals, and compare with the corresponding percentages given by the Empirical Rule and Tchebysheff's Theorem. (Round your answers to three decimal places.) Interval Actual Percentage Tollebyelleff Empirical at least as 68% at least 75% e 95 '1 % at least 89% as 99.7%