In a certain distribution, the mean is 50 with a standard deviation of 6 . Use Chebyshev's theorem to tell the probabilitythat a number lies in the following interval. Round your results to the nearest whole percent.
-Less than 20 or more than 80
A) At most $4 \%$
B) At most $6 \%$
C) At most $2 \%$
D) At most $1 \%$

Question

Quizplus · Accepted Answer

Chebyshev's theorem states that at least $1 - \frac{1}{k^2}$ of the data lies within $k$ standard deviations from the mean. Here, $k = \frac{80-50}{6} = 5$. So, at least $1 - \frac{1}{5^2} = 0.96$ or 96% of the data lies between 20 and 80, meaning at most 4% lies outside this range.

In a Certain Distribution, the Mean Is 50 with a Standard