The ages of the members of a gym have a mean of 48 years and a standard deviation of 10 years. What can you conclude from Chebyshev's theorem about the percentage of gym members aged between 26 and 70?

A) The percentage is at least 79.3%
B) The percentage is approximately 54.5%
C) The percentage is at least 54.5%
D) The percentage is at most 79.3%

Question

The ages of the members of a gym have a mean of 48 years and a standard deviation of 10 years. What can you conclude from Chebyshev's theorem about the percentage of gym members aged between 26 and 70?

A) The percentage is at least 79.3%
B) The percentage is approximately 54.5%
C) The percentage is at least 54.5%
D) The percentage is at most 79.3%

Quizplus · Accepted Answer

Chebyshev's theorem states that for any distribution, at least (1 - 1/k^2) of the data lies within k standard deviations of the mean. Here, k = (70-48)/10 = 2.2 and (48-26)/10 = 2.2. So, at least (1 - 1/2.2^2) ≈ 79.3% of the data is within this range.

The Ages of the Members of a Gym Have a Mean