2010 US Gas Prices: Insights with Chebyshev’s Inequality

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Chebyshev’s Inequality In December 2010, the average price of regular unleaded gasoline excluding taxes in the United States was $3.06 per gallon, according to the Energy Information Administration. Assume that the standard deviation price per gallon is $0.06 per gallon

(a) Chebyshev’s Inequality:

\(\begin{array}{l}\text{- } \bar{x}-k s< \text{ values } <\bar{x}+k s\\
\text{- Proportion: } \left(1-\frac{1}{K^{2}}\right) \times 100 \%\end{array}\)

Where, \(\bar{x}=\text { Mean }\)

              k  = Number of Standard deviation

              s  = Standard deviation

Here, the minimum percentage of gasoline stations had prices within 3 standard deviations of the mean

Hence k = 3

Then, \(\left(1-\frac{1}{K^{2}}\right) \times 100 \%=\left(1-\frac{1}{3^{2}}\right) \times 100 \%=0.8888 \times 100 \%=88.88 \%\)

Therefore, 88.88% of gas stations have prices within 3 standard deviations of the mean.