Solve the problem.
-The heights of the adults in one town have a mean of 67.5 inches and a standard deviation of 3.4 inches. What can you conclude from Chebyshev's theorem about the percentage of adults in the town whose heights are between 60.7 and 74.3 inches?
A)The percentage is at least 75%
B)The percentage is at most 95%
C)The percentage is at least 95%
D)The percentage is at most 75%

Question

Quizplus · Accepted Answer

Chebyshev's theorem states that for any dataset (regardless of distribution), at least $1 - \frac{1}{k^2}$ of the data falls within $k$ standard deviations from the mean. Here, the range from 60.7 to 74.3 inches is $2 \times 3.4$ inches (or $2$ standard deviations) from the mean (67.5 inches). Thus, $k = 2$, and applying Chebyshev's theorem gives $1 - \frac{1}{2^2} = 1 - \frac{1}{4} = \frac{3}{4}$, or 75%. Therefore, at least 75% of the adults' heights are within this range.

Solve the Problem. -The Heights of the Adults in One Town Have a Town