From a sample with $n=16$, the mean number of pets per household is 2 with a standard deviation of 1 pet. Using Chebychev's Theorem, determine at least how many of the households have 0 to 4 pets. At least $\square$ of the households have Oto 4pets. (Simplify your answer.)
Solution
Step 1 ：Given a sample with \(n=16\), the mean number of pets per household is 2 with a standard deviation of 1 pet.
Step 2 ：We are asked to determine at least how many of the households have 0 to 4 pets.
Step 3 ：We can use Chebyshev's theorem, which states that at least \(1 - 1/k^2\) of the data lies within \(k\) standard deviations of the mean for all \(k>1\).
Step 4 ：In this case, we want to find the proportion of households that have between 0 and 4 pets, which is 2 standard deviations away from the mean (\(2 - 2*1 = 0\) and \(2 + 2*1 = 4\)). So, we can use \(k=2\) in Chebyshev's theorem to find the answer.
Step 5 ：Substituting \(k = 2\) into the formula, we get the proportion as \(1 - 1/2^2 = 0.75\).
Step 6 ：Converting this proportion to percentage, we get \(0.75 * 100 = 75\%\).
Step 7 ：Final Answer: At least \(\boxed{75\%}\) of the households have 0 to 4 pets.
