For k 1, Chebyshev's theorem is useful in estimating the proportion of observations that fall within ________. A) k standard deviations from the mean B) k² standard deviations from the mean C) (1 - 1/k) standard deviations from the mean D) (1 - 1/k²) standard deviations from the mean

Question

For k > 1, Chebyshev's theorem is useful in estimating the proportion of observations that fall within ________. A) k standard deviations from the mean B) k² standard deviations from the mean C) (1 - 1/k) standard deviations from the mean D) (1 - 1/k²) standard deviations from the mean

Quizplus · Accepted Answer

Chebyshev's theorem states that for any distribution, at least (1 - 1/k^2) of the observations fall within k standard deviations from the mean. Therefore, answer choice A is the only option that correctly reflects this theorem.

For K > 1, Chebyshev's Theorem Is Useful in Estimating