Question

From a sample with n=12, the mean number of television per household is 3 with a standard deviation of 1 television. Using Chebychev Theorem,determine at least how many of the households have between 1 and 5 televisons

Answer 1

9

Explanation:

Chebyshev's Theorem states that for any given sample, at least 1 - 1/k^2 of the data falls within k standard deviations from the mean.

Let's use k = 2. Then, at least 1 - 1/2^2 = 1 - 1/4 = 3/4 of the households should have between 3 - 2 = 1 and 3 + 2 = 5 televisions.

So, at least 12 * 3/4 = 9 of the households in the sample have between 1 and 5 televisions.