Question

a forester measured 29 of the trees in a large woods that is up for sale. he found a mean diameter of 10.2 inches and a standard deviation of 4.8 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.

b) what size would you expect the central 95% of all tree diameters to be?
using the 68 - 95 - 99.7 rule, the central 95% of the tree diameters are between \\( \square \\) inches and \\( \square \\) inches.
(do not round. type integers or decimals.)

Explanation:

Step1: Recall the 68 - 95 - 99.7 rule

The 68 - 95 - 99.7 rule for a normal distribution states that approximately 95% of the data lies within \(\mu\pm2\sigma\).

Step2: Calculate the lower and upper bounds

Given \(\mu = 10.2\) and \(\sigma=4.8\).
The lower bound is \(\mu - 2\sigma=10.2-2\times4.8\).

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The upper bound is \(\mu + 2\sigma=10.2 + 2\times4.8\).

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Answer:

The central 95% of the tree diameters are between \(0.6\) inches and \(19.8\) inches.