Final answer:
Chobyshev's theorem states that at least 87.2% of gym members are aged between 16 and 72 years.
Step-by-step explanation:
Chobyshev's theorem states that for any distribution, regardless of its shape, at least 1 - (1/k^2) of the data will fall within k standard deviations of the mean, where k is any positive number greater than or equal to 1. In this case, the mean age is 44 years and the standard deviation is 10 years. To find the percentage of gym members aged between 16 and 72, we need to determine how many standard deviations away from the mean these ages are.
First, we calculate the distance from the mean to each boundary: (16 - 44)/10 = -2.8 and (72 - 44)/10 = 2.8. The absolute value of these distances is 2.8, so we can conclude that the ages of gym members aged between 16 and 72 are within 2.8 standard deviations of the mean.
Using Chobyshev's theorem, we can determine that at least 1 - (1/2.8^2) = 1 - (1/7.84) = 0.872 or 87.2% of the gym members are aged between 16 and 72 years. Therefore, the correct option is A. The percentage is at least 87.2%.