Question

From a sample with n = 36, the mean number of televisions per household is 3 with a standard deviation of 1 television. Using Chebyshev's Theorem, determine at least how many of the households have between 1 and 5 televisions. At least ___ of the households have between 1 and 5 televisions. (Simplify your answer.)

Answer 1

At least 75% of the households have between 1 and 5 televisions.

Step-by-step explanation:

To determine how many households have between 1 and 5 televisions using Chebyshev's Theorem, we need to calculate the range within k standard deviations from the mean. Chebyshev's Theorem states that at least 1 - (1/k^2) of the data falls within k standard deviations from the mean. In this case, the mean is 3 and the standard deviation is 1, so k = (5-3)/1 = 2. Therefore, at least 1 - (1/2^2) = 1 - (1/4) = 3/4 = 75% of the households have between 1 and 5 televisions.