From a sample with nequals=20​, the mean number of televisions per household is 4 with a standard deviation of 1 television. Using​ Chebychev's Theorem, determine at least how many of the households have between 2 and 6 televisions.

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Question:

From a sample with nequals=20​, the mean number of televisions per household is 4 with a standard deviation of 1 television. Using​ Chebychev's Theorem, determine at least how many of the households have between 2 and 6 televisions.

Answers

Answer: There are atleast 15 households that have between 2 and 6 televisions.Step-by-step explanation:Since we have given that n = 20mean number of televisions per household = 4Standard deviation = 1we need to find the number of the households have between 2 and 6 television.First we check the within numbers.[tex]\mu-x_1=4-2=2\\\\x_2-\mu=6-4=2[/tex]so, we can say that there are 2 television which is within numbers.So, now, we will find the value of k:[tex]k=\dfrac{\text{within number}}{\text{Standard deviation}}\\\\k=\dfarc{2}{1}=2[/tex]Using the Chebychev's theorem, we get that [tex]1-\dfrac{1}{k}^2\\\\=1-\dfrac{1}{2^2}\\\\=1-\dfrac{1}{4}\\\\=\dfrac{4-1}{4}\\\\=\dfrac{3}{4}[/tex]so, the number of the households would be[tex]\dfrac{3}{4}\times 20\\\\=3\times 5\\\\=15[/tex]Hence, there are atleast 15 households that have between 2 and 6 televisions.

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