Question

The ages of the members of a gym have a mean of 45 years and a standard deviation of 11 years What can you conclude from Chebyshev's theorem about the percentage of gym members aged between 17 and 777 A) The percentage is approximately 89% B) The percentage is at least 75% C) The percentage is at least 89% D) The percentage is at most 89%

Answer 1

option D) The percentage is at most 89%

Explanation:

mean, u = 45

standard deviation, s = 11

%age of members between 17 and 77 = ?

chebyshev's theorem = 1 - 1/k²

according to the question,

u + ks = 77 (the upper limit given to us)

u - ks = 17 (the lower limit given to us)

let's find k now,

u + ks = 77

45 + k(11) = 77

11k = 32

k = 32/11 = 2.909....

by substituting the value in the chebyshev's theorem,

1 - 1/(2.91)² = 1 - 1/8.4681

= 1 - .1181 = .8819

= 88.19% = 88%

thus, the percentage of gym members aged between 17 and 77 is at most 89%