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Thread: Chebyshev's Theorem and Empirical Rule

  1. #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. #2
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    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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