A severe drought affected several western states for 3 years. A Christmas tree farmer is worried about thedroughtʹs effect on the size of his trees. To decide whether the growth of the trees has been retarded, the farmerdecides to take a sample of the heights of 25 trees. Typically trees of this age have a mean height of 65 incheswith a standard deviation of 9 inches. Assuming the distribution is bell shaped, where do you expect middle95% of the tree heights to fall?
A) between 47 and 83 inches tall
B) between 56 and 74 inches tall
C) between 38 and 92 inches tall
D) over 56 inches tall

Question

Quizplus · Accepted Answer

Using the empirical rule for a bell-shaped distribution, the middle 95% of the data falls within two standard deviations of the mean. The mean is 65 inches, and the standard deviation is 9 inches. Therefore, two standard deviations from the mean is 65 ± 2(9) = 65 ± 18, which gives us a range of 47 to 83 inches.

A Severe Drought Affected Several Western States for 3 Years