Question

The ages of the members of a gym have a mean of 44 years and a standard deviation of 12 years. What can you conclude about Chebyshev's theorem about the percentage of gym members aged between 8 and 80?

A) Chebyshev's theorem can't be applied in this case.
B) At least 75% of the members are between 8 and 80 years old.
C) At least 25% of the members are between 8 and 80 years old.
D) At least 88.9% of the members are between 8 and 80 years old.

Answer 1

Chebyshev's theorem states that at least 75% of the data falls within three standard deviations of the mean. In this case, the mean age of gym members is 44 years with a standard deviation of 12 years. Therefore, at least 75% of the gym members are between 8 and 80 years old.

Step-by-step explanation:

Chebyshev's theorem states that for any distribution, regardless of its shape, at least k percent of the data falls within k standard deviations of the mean.

In this case, the mean age is 44 years and the standard deviation is 12 years. To find the percentage of gym members aged between 8 and 80, we need to determine the number of standard deviations away from the mean those ages are.

The distance between 8 and 44 is (44 - 8) / 12 = 3 standard deviations below the mean. The distance between 80 and 44 is (80 - 44) / 12 = 3 standard deviations above the mean.

According to Chebyshev's theorem, at least 75% of the data falls within 3 standard deviations of the mean. Therefore, we can conclude that at least 75% of the gym members are between 8 and 80 years old.