Question

A forester measured 28 of the trees in a large woods that is up for sale. He found a mean diameter of 10.4 inches and a standard deviation of 4.4 inches. Suppose that these trees provide an accurate description of the whole forest and that a Normal model applies. a) Choose the correct Normal model for tree diameters. A. B. C. b) What size would you expect the central 68% of all tree diameters to be? Using the 68-95-99.7 rule, the central 68% of the tree diameters are between ____ inches and _____ inches. (Do not round. Type integers or decimals.) c) About what percent of the trees should have diameters below 1.6 inches? Using the 68-95-99.7 rule, about _____ % of the trees should have diameters below 1.6 inches. (Do not round. Type an integer or a decimal.) Click to select your answer(s).

Answer 1

Answer:

a) Attachment

b) 6 to 14.8 in

c) 2.5%

Step-by-step explanation:

Given:

- The mean is u = 10.4 in

- The standard deviation s.d = 4.4

- Sample size n = 28

Find:

- Choose the correct Normal model for tree diameters. A. B. C.

- What size would you expect the central 68% of all tree diameters to be?Using the 68-95-99.7 rule, the central 68% of the tree diameters are between ____ inches and _____ inches.

- About what percent of the trees should have diameters below 1.6 inches?

Solution:

- The central 68% lies within two s.d from mean.

                                  10.4 + 1*4.4 = 14.8

                                  10.4 - 1*4.4 = 6

Hence, the central 68% are between 6 and 14.8 inches.

- The central 95% lies within two s.d from mean.

                                  10.4 + 2*4.4 = 19.2

                                  10.4 - 2*4.4 = 1.6

- The central 95% are between 1.6 and 19.2 inches.

- Hence, P ( X < 1.6) = (1 - 0.95)/2 = 0.025 or 2.5%