Solve the problem.
-The ages of the members of a gym have a mean of 47 years and a standard deviation of 10 years. What can you conclude from Chebyshev's theorem about the percentage of gym members aged between 32 and 62?
A)The percentage is approximately 33.3%
B)The percentage is at most 55.6%
C)The percentage is at least 33.3%
D)The percentage is at least 55.6%

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 values will fall within $k$ standard deviations of the mean. Here, the range from 32 to 62 years is 15 years on either side of the mean (47), which is 1.5 standard deviations ($k = 1.5$). Applying Chebyshev's theorem, at least $1 - \frac{1}{1.5^2} = 1 - \frac{1}{2.25} = \frac{4}{9}$ or approximately 55.6% of the gym members' ages fall within this range.

Solve the Problem. -The Ages of the Members of a Gym Have a Gym