From a sample with nequals12​, the mean number of televisions per household is 2 with a standard deviation of 1 television. Using​ Chebychev

Question

From a sample with nequals12​, the mean number of televisions per household is 2 with a standard deviation of 1 television. Using​ Chebychev’s Theorem, determine at least how many of the households have between 0 and 4 televisions.

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Kaylee 3 days 2021-10-10T06:35:58+00:00 1 Answer 0

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    2021-10-10T06:37:26+00:00

    Answer:

    At least 9 households have between 0 and 4 televisions.

    Step-by-step explanation:

    According to the Chebychev’s theorem,

    P(|X-\mu|\leq k\sigma)\geq 1-\frac{1}{k^{2}}

    Here k is a constant.

    Given:

    μ = 2

    σ = 1

    n = 12

    Using the Chebychev’s theorem determine the probability of households having between 0 and 4 televisions as follows:

    P(0\leq X\leq 4)=P(0-2\leq (X-\mu) \leq 4-2 )\\=P(-2\leq (X-\mu) \leq 2)\\=P(|X-\mu|\leq (2\times 1))\\\geq 1-\frac{1}{2^{2}} =1-\frac{1}{4} =1-0.25=0.75

    This implies that at least 75% of the 12 households have between 0 and 4 televisions.

    Compute 75% of n = 12 as follows:

    75\%\ of\ 12=\frac{75}{100}\times12= 9

    Thus, at least 9 households have between 0 and 4 televisions.

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