Reference no: EM132855209

To estimate 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-by-50 foot squares. Seventy 50-by-50 foot squares were chosen via a simple random sample of all squares in the tract, and the selected trees were counted in each tract. The data are listed here:

7, 8, 7, 10, 4, 8, 6, 8, 9, 10,
9, 6, 4, 9, 10, 9, 8, 8, 7, 9,
3, 9, 5, 9, 9, 8, 7, 5, 8, 8
10, 2, 7, 4, 8, 5, 10, 7, 7, 7
9, 6, 8, 8, 8, 7, 8, 9, 6, 8
6, 11, 9, 11, 7, 7, 11, 7, 9, 13
10, 8, 8, 5, 9, 9, 8, 5, 9, 8

A) Calculate the sample mean as an estimate of u, the mean number of timber trees for all 50-by-50 foot squares in the tract.

B) Calculate the sample standard deviation (s) for the data. Construct intervals, calculate the percentage of squares falling into each of the three intervals, and compare with the corresponding percentages given by the empirical rule.

D) In the population, are the numbers of trees per 50-by-50-foot square normally distributed? Justify the answer.