# Thread: Chebyshev's Theorem and Empirical Rule

1. ## Chebyshev's Theorem and Empirical Rule

I am having a hard time understanding the following. The information leading up to the question goes as follows:
" A major cab company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be \$26.49, with a standard deviation of \$3.35. Based on this information, complete the following statements about the distribution of the company's fares from the airport to the hotel."

The question states that:
"According to Chebyshev's theorem,at least _% of the fares lie between 19.79 dollars and 33.19 dollars."

My question is Chebyshev's theorem states [100(1-1/ksquared)]%. It says to first find the standard deviations first then the theorem, which is:

19.79-26.49/3.35=-2 and 33.19-26.49/3.35=2.

I am not understanding where the 2 and -2 are coming from. Can anyone please help me to understand this in the simplest terms. PLEASE!!!!!

Thank you.

2. 19.79-26.49/3.35=-2 means that 19.79 is 2 standard deviations below the mean

33.19-26.49/3.35=2 means that 33.19 is 2 standard deviations above the mean

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