The heights of the adults in one town have a mean of 67.1 inches and a standard deviation of 3.5 inches. What can you conclude from Chebyshev's theorem about the percentage of adults
In the town whose heights are between 60.1 and 74.1 inches?
A)The percentage is at most 75%.
B)The percentage is at most 95%.
C)The percentage is at least 95%.
D)The percentage is at least 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 within a dataset will fall within k standard deviations from the mean. Here, the range from 60.1 to 74.1 inches is 7 inches (or 2 standard deviations) away from the mean on either side, since $67.1 - 60.1 = 74.1 - 67.1 = 7$ inches and $7 \div 3.5 = 2$. Applying Chebyshev's theorem with $k = 2$, we get at least $1 - \frac{1}{2^2} = 1 - \frac{1}{4} = \frac{3}{4} = 75\%$ of the data falls within this range.

The Heights of the Adults in One Town Have a Mean