Answer
a. $96\%$
b. $94\%$
Work Step by Step
Chebyshev’s theorem The proportion of values from a data set that will fall within k
standard deviations of the mean will be at least $1−1/k^2$, where k is a number greater
than 1 (k is not necessarily an integer).
32. The mean of a distribution is 20 and the standard
deviation is 2. Use Chebyshev’s theorem.
a. At least what percentage of the values will fall
between 10 and 30? $k=5, 1-1/5^2=0.96$ or $96\%$
b. At least what percentage of the values will fall
between 12 and 28? $k=4, 1-1/4^2=0.94$ or $94\%$
