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Using the 68-95-99.7 rule, what percentage of the trees should have diameters below 5.8 inches?

A. 68%
B. 95%
C. 99.7%
D. 32%

Answer :

Final answer:

In applying the 68-95-99.7 rule, it's likely that more than 68% but not as conclusive as b. 95% or c. 99.7% of the trees have diameters below 5.8 inches, without additional data regarding the mean and standard deviations of the tree diameters.

Explanation:

Using the 68-95-99.7 rule, which is a shorthand for the empirical rule or the three-sigma rule in statistics, we can determine about what percentage of data falls within certain standard deviations from the mean in a normal distribution. Specifically, the rule states that approximately 68% of data falls within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations from the mean.

If we need to find the percentage of trees that have diameters below 5.8 inches and assuming that 5.8 inches is not more than three standard deviations away from the mean, and the distribution is normal, then more than 68% of the data would be expected to fall below this point but not as much as 95%. Hence, the correct answer would likely be that more than 68% of the trees have diameters below 5.8 inches, which eliminates options a) and d).

Without additional information regarding the mean and standard deviation, we cannot definitively conclude whether 95% or 99.7% of the trees have diameters below this value. The exact percentage could fall between option b) 95% and option c) 99.7%, but it is clear that the answer is not strictly 68% or 32%.

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