Question

From a sample with n=36, 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.

At least ____ of the households have between 0 and 4 televisions.
(Simplify your answer.)

Answer 1

Chebyshev's Theorem states that for any dataset with a mean and standard deviation, at least 1 - (1/k^2) of the data will lie within k standard deviations of the mean.

In this case, we're looking for households that have between 0 and 4 televisions, which is 4 - 0 = 4 - 2 = 2 standard deviations from the mean of 2 televisions.

So, using Chebyshev's Theorem, we can calculate that at least 1 - (1/2^2) = 1 - (1/4) = 3/4 or 75% of the households have between 0 and 4 televisions.

At least 75% of the households have between 0 and 4 televisions.