Solved: Chebyshev’s Inequality According to the U.S.

Step 1 of 3

According to the U.S. Census Bureau, the mean of the commute time to work for a resident of Boston, Massachusetts, is 27.3 minutes. Assume that the standard deviation of the commute time is 8.1 minutes to answer the following:

(a)  Chebyshev’s Inequality:

-  \(\bar{x}-k s<\text { values }<\bar{x}+k s\)

-    Proportion: \(\left(1-\frac{1}{k^{2}}\right) \times 100 \%\) 

Where, \(\bar{x}\) = Mean

k  = Number of Standard deviation

s  = Standard deviation

Here, the percentage of commuters in Boston has a commute time within 2 standard deviations of the mean

Hence k = 2

Then, \(\left(1-\frac{1}{k^{2}}\right) \times 100 \%=\left(1-\frac{1}{2^{2}}\right) \times 100 \%=0.75 \times 100 \%=75 \%\)

Therefore, 75% of commuters in Boston has a commute time within 2 standard deviations of the mean.