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26 March, 20:21

You take a sample of rents of 182 apartments in San Francisco and find that the mean rent is $4000 per month and the standard deviation is $1000 per month. According to Chebyshev's Theorem, what percentage of the rents in your sample fall between $1000 and $7000 per month? At least 89%

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Answers (2)
  1. 26 March, 21:48
    0
    89%

    Explanation:

    according to Chebyshev's theorem, for any k > 1, at least [1 - (1/k^2) ] of the data will lie within k standard deviations of the mean. Therefore, Chebyshev's theorem formula can be given as follows:

    Chebyshev's theorem formula = 1 - (1/k^2) ... (1)

    In order to fing k, we proceed as follows:

    1. Subtract the mean of rents from the larger rent value,

    That is, $7,000 - $4,000 = $3,000

    2. Divide the difference of $3,000 above by the standard deviation to obtain k as follows:

    k = $3,000 : $1000 = 3

    3. Substitute 3 for k in equation (1) as follows:

    Chebyshev's theorem formula = 1 - (1/3^2)

    = 1 - (1/9)

    = 1 - 0.11

    = 0.89

    If we multiply 0.89 by 100, we have 89%.

    Therefore, 89% of the rents in the sample will fall between $1000 and $7000 per month.
  2. 26 March, 23:50
    0
    Answer: Between $2,000 and $6,000

    Explanation:

    The probability must be between $2,000 and $6,000, that is, k=3, the standard deviation of the mean.

    ∴ 1 - 1/k² = 1 - 1/3² = 9 - 1/9 = 8/9

    Hence, 8/9 of 100% = 89%

    The probability between $2,000 and $6,000 must be at least 89%
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