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.
-Between 26 and 74
A)A t least $94 \%$
B) At least $90 \%$
C) At least $96 \%$
D) At least $93 \%$

Question

Quizplus · Accepted Answer

Chebyshev's theorem states that at least $1 - \frac{1}{k^2}$ of the data lies within $k$ standard deviations of the mean. Here, $k = \frac{74-50}{6} = 4$ and $k = \frac{50-26}{6} = 4$, so at least $1 - \frac{1}{4^2} = 1 - \frac{1}{16} = 0.9375$ or 94% of the data lies between 26 and 74.

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