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.
o a.
o b.
o c.

Explanation:

Step1: Recall the properties of normal distribution

In a normal distribution, about 68% of the data lies within \( \mu\pm\sigma\), about 95% lies within \( \mu\pm2\sigma\), and about 99.7% lies within \( \mu\pm3\sigma\).

Step2: Calculate the values for \( \mu\pm\sigma\), \( \mu\pm2\sigma\), \( \mu\pm3\sigma\)

Given \( \mu = 10.2\) and \( \sigma=4.8\).

• For \( \mu-\sigma\): \(10.2 - 4.8=5.4\)
• For \( \mu+\sigma\): \(10.2 + 4.8 = 15.0\)
• For \( \mu - 2\sigma\): \(10.2-2\times4.8=10.2 - 9.6 = 0.6\)
• For \( \mu+2\sigma\): \(10.2 + 2\times4.8=10.2+9.6 = 19.8\)
• For \( \mu-3\sigma\): \(10.2-3\times4.8=10.2 - 14.4=- 4.2\)
• For \( \mu+3\sigma\): \(10.2+3\times4.8=10.2 + 14.4=24.6\)

Answer:

B.