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).

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%

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