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March 25, 2017

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1. The mean monthly mortgage paid by all home owners in a town is $2365 with a standard deviation of $340. a) Using Chebyshev’s theorem, find at least what percentage of all home owners in this town pay a monthly mortgage of (i) $1685 to $3045 & (ii) $1345 to $3385
b) Using Chebyshev’s theorem, find the interval that contains the monthly mortgage payments of at least 84% of all home owners in this town.

  • Statistics - ,

    Chebyshev's theorem says:
    1. Within two standard deviations of the mean, you will find at least 75% of the data.
    2. Within three standard deviations of the mean, you will find at least 89% of the data.

    Part (i) is within two standard deviations of the mean.
    Part (ii) is within three standard deviations of the mean.

  • Statistics - ,

    There is a formula you can use to find part b).

    1 - (1/k^2) = .84 (or 84%)
    k = 2.5 (standard deviations)

    Therefore, find the amounts within 2.5 standard deviations of the mean. Remember that one standard deviation is equal to $340.

    I'll let you take it from here.

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