If nothing is known about the shape of a distribution, what percentage of the observations fall within 3 standard deviations of the mean?
A)approximately 99.7%
B)at most 11%
C)approximately 0.3%
D)at least 89%

Question

Quizplus · Accepted Answer

According to Chebyshev's theorem, for any distribution, at least 1 - 1/k^2 of the data falls within k standard deviations of the mean. For k=3, this means at least 1 - 1/9 = 89% of the observations fall within 3 standard deviations of the mean.

If Nothing Is Known About the Shape of a Distribution