Engineers Initially Surveyed the Territory of Iowa in the 1830's

Essay

Engineers initially surveyed the Territory of Iowa in the 1830's, and they were verycareful to take note of the trees and vegetation. The sample of hickory tree diametersfrom the original survey of what is now Linn County, is presented in the stem andleaf plot below. The display uses five lines for each stem. Thus, "1t|" is the stem fordiameters of 12 and 13, "1f|" for 14 and 15, "1s|" for 16 and 17, and so on. (The "t"then stands for leaves that are twos and threes, the "f" for leaves of fours and fives,etc.)The mean diameter of the 73 hickory trees in this sample is 11.849 inches, and thestandard deviation is 3.995 inches.
(a) What is the approximate diameter of a hickory tree at the 20th percentile in thisdistribution?

(b) According to the Empirical Rule, approximately 68% of hickory tree diametersare between what two values?