A severe drought affected several western states for 3 years. A Christmas tree farmer is worried about the drought's effect on the size of his trees. To decide whether the growth of the trees has been retarded, the farmer decides to take a sample of the heights of 25 trees. Typically trees of this age have a mean height of 65 inches with a standard deviation of 9 inches. Assuming the distribution is bell shaped, where do you expect middle 95% of the tree heights to fall?
A) between 47 and 83 inches tall
B) between 38 and 92 inches tall
C) between 56 and 74 inches tall
D) over 56 inches tall

Question

Quizplus · Accepted Answer

According to the empirical rule (68-95-99.7 rule) for a bell-shaped distribution, approximately 95% of the data falls within 2 standard deviations of the mean. Given a mean of 65 inches and a standard deviation of 9 inches, 2 standard deviations from the mean would be from 65 - 2(9) = 47 inches to 65 + 2(9) = 83 inches.

A Severe Drought Affected Several Western States for 3 Years