Use the Empirical Rule to Describe Data That Are Bell Shaped
-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 56 and 74 inches tall
C) between 38 and 92 inches tall
D) over 56 inches tall

Question

Quizplus · Accepted Answer

The Empirical Rule states that for a bell-shaped distribution, approximately 95% of the data falls within 2 standard deviations of the mean. The mean height is 65 inches, and the standard deviation is 9 inches. Calculating 2 standard deviations from the mean gives us 65 - 2(9) = 47 inches and 65 + 2(9) = 83 inches. Therefore, we expect the middle 95% of the tree heights to fall between 47 and 83 inches tall.

Use the Empirical Rule to Describe Data That Are Bell 95%95 \%95%

Use the Empirical Rule to Describe Data That Are Bell $95 \%$