To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and cou

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To Estimate The Amount Of Lumber In A Tract Of Timber An Owner Randomly Selected Seventy 50 By 50 Foot Squares And Cou 1 (176.56 KiB) Viewed 70 times

To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted the number of trees with diameters exceeding 12 inches in each square. The data are listed here. 5 7 5 7 8 10 9 6 3 8 10 9 8 8 69 39 9 6 10 10 9 8 5 87 11 16 48 5 10 6 6 6 97 98 98 89 58 7 11 10 10 8712 8 10 13 11995 10885 10 8 1 i USE SALT Frequency of lumber Frequency of lumber (a) Construct a relative frequency histogram to describe the data. Frequency of lumber 0.40 0.35 0.30 " 0.25 0.20 0.15 0.10 0.05 Relative Frequency 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 Relative Frequency 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 4 5 7 8 amount of lumber 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 amount of lumber 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 amount of lumber 0 00 Frequency of lumber Relative Frequency 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 amount of lumber (b) Calculate the sample mean x as an estimate of the mean number of trees for all 50-by-50-foot squares in the tract. (Round your answer to three decimal places.) x = timber trees (c) Calculate s for the data. (Round your answer to three decimal places.) S- timber trees Construct the intervals x 5, % 25, and x + 3s. 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 interval values to three decimal places. Round actual percentages to two decimal places.) Interval Actual Percentage Tchebysheff Empirical Xus to 10.043 % at least % 258% x + 25 3.358 to % at least 75% % X+ 35 1.130 to % at least 89% 99.7%