Question

In 2010, the average price of gasoline in the U.S. was $3.06 per gallon with a standard deviation price per gallon at $0.06 per gallon. Use Chebyshev's Theorem to find the percentage of gasoline stations that had prices within 3 standard deviation of the mean

Answer 1

Use Chebyshev's Theorem to 88.89 % the percentage of gasoline stations that had prices within 3 standard deviation of the mean.

What is the Chebyshev's theorem?

• Chebyshev's Theorem estimates the minimum proportion of observations that fall within a specified number of standard deviations from the mean.
• This theorem applies to a broad range of probability distributions.
• Chebyshev's Theorem is also known as Chebyshev's Inequality.

By Chebyshev's inequality, for any distribution at least

$(1 -\frac{1}{k^{2} } )$ * 100 percentage of values falls within k standard deviation about mean .

here k=3 . Apply this to equation and find percentage that falls within 3 standard deviation about mean.

$( 1 - \frac{1}{3^{2} } ) * 100$ =  88.89

So,  88.89 % of gasoline station had price within 3 standard deviation about mean .

Learn more about Chebyshev's inequality

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