(Solved): To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50 -by-5 ...

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. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline 8 & 9 & 6 & 10 & 3 & 7 & 7 & 8 & 8 & 9 \\ \hline 8 & 5 & 5 & 9 & 10 & 9 & 8 & 9 & 8 & 9 \\ \hline 4 & 8 & 5 & 10 & 8 & 9 & 6 & 4 & 7 & 8 \\ \hline 10 & 1 & 8 & 3 & 7 & 6 & 11 & 6 & 8 & 8 \\ \hline 8 & 6 & 7 & 8 & 8 & 6 & 8 & 8 & 5 & 9 \\ \hline 7 & 12 & 10 & 11 & 7 & 6 & 10 & 8 & 10 & 13 \\ \hline 9 & 7 & 9 & 5 & 8 & 10 & 7 & 6 & 8 & 7 \\ \hline \end{tabular} (b) Calculate the sample mean $$\stackrel{?}{x}$$ 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.) $$\stackrel{?}{x}=7.643$$ timber trees (c) Calculate $$s$$ for the data. (Round your answer to three decimal places.) $$s=2.120$$ timber trees Construct the intervals $$\stackrel{?}{x}\pm s,\stackrel{?}{x}\pm 2s$$, and $$\stackrel{?}{x}\pm 3s$$. Calculate the percentage of squares falling into each of the three intervals, and compare with the corresponding percentages giv by the Empirical Rule and Tchebysheff's Theorem. (Round your interval values to three decimal places. Round actual percentages to two decimal places.)