The heights of the adults in one town have a mean of 66.8 inches and a standard deviation of 3.4 inches. What can you conclude from Chebyshev's rule about the percentage of adults in the town Whose heights are between 56.6 and 77 inches?
A)The percentage is at least 99.7%
B)The percentage is at most 99.7%
C)The percentage is at least 89%
D)The percentage is at most 89%

Question

The heights of the adults in one town have a mean of 66.8 inches and a standard deviation of 3.4 inches. What can you conclude from Chebyshev's rule about the percentage of adults in the town Whose heights are between 56.6 and 77 inches? 
A)The percentage is at least 99.7%
B)The percentage is at most 99.7%
C)The percentage is at least 89%
D)The percentage is at most 89%

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 $k$ standard deviations from the mean. Here, $56.6$ and $77$ inches are $3$ standard deviations away from the mean ($66.8 \pm 3 \times 3.4$). So, $k = 3$, and at least $1 - \frac{1}{3^2} = 1 - \frac{1}{9} = \frac{8}{9} = 88.8\%$ of the data falls within this range. Rounding up, we get at least $89\%$.

The Heights of the Adults in One Town Have a Mean