Chapter 2.5, Problem 2.31E

Timber Tracts To estimate the amount of lumber in a tract of timber, an owner decidedto count the number of trees with diameters exceeding12 inches in randomly selected 50-by-50-foot squares.Seventy 50-by-50-foot squares were chosen, and theselected trees were counted in each tract. The data arelisted here:

1. Construct a relative frequency histogram to describethe data.
2. Calculate the sample mean $\bar{x}$ as an estimate of $\mu$, themean number of timber trees for all 50-by-50-footsquares in the tract.
3. Calculate s for the data. Construct the intervals $\bar{x}\pm s,\bar{x}\pm 2s,$ and $\bar{x}\pm 3s.$Calculate the percentageof squares falling into each of the three intervals,and compare with the corresponding percentagesgiven by the Empirical Rule and Tchebysheff’sTheorem.