For any distribution,the percent of observations that lie within four standard deviations of the mean is:
A)93.75% or more.
B)93.75% or less.
C)6)25% or more.
D)6)25% or less.

Question

Quizplus · Accepted Answer

For any distribution, Chebyshev's theorem states that at least 1-(1/k^2) of the observations will lie within k standard deviations of the mean. So, for k=4, at least 1-(1/4^2) = 1-0.0625 = 0.9375, or 93.75% of the observations will lie within 4 standard deviations of the mean. Therefore, the best choice is A, which states that the percent of observations that lie within four standard deviations of the mean is 93.75% or more.

For Any Distribution,the Percent of Observations That Lie Within Four