To assist in estimating the amount of lumber in a tract of timber, an owner decided to count the number of trees with diameters exceeding 12 inches in randomly selected 50 x 50-foot squares. Seventy 50 x 50 squares were randomly selected from the tract and the number of trees (with diameters in excess of 12 inches) was counted for each. The data are as follows:
a. Construct a relative frequency histogram to describe these data.
b. Calculate the sample mean y as an estimate of m, the mean number of timber trees with diameter exceeding 12 inches for all 50 3 50 squares in the tract.
c. Calculate s for the data. Construct the intervals (y-bar ± s), (y-bar ± 2s), and (y-bar ± 3s). Count the percentages of squares falling in each of the three intervals, and compare these percentages with the corresponding percentages given by the Empirical Rule.