Question

from a sample with \\(n = 28\\), the mean number of pets per household is 4 with a standard deviation of 1 pet. using chebychevs theorem, determine at least how many of the households have 2 to 6 pets.

at least of the households have 2 to 6 pets.
(simplify your answer.)

Explanation:

Identify given parameters

Using the Chebyshevs Theorem knowledge point

$$
LATEXBLOCK0
$$

Determine standard deviations from mean

Using the Chebyshevs Theorem knowledge point

$$
LATEXBLOCK1
$$

Calculate minimum proportion

Using the Chebyshevs Theorem knowledge point

$$ P \ge 1 - \frac{1}{k^2} = 1 - \frac{1}{2^2} = 1 - \frac{1}{4} = \frac{3}{4} $$

Calculate minimum number of households

Using the Chebyshevs Theorem knowledge point

$$
LATEXBLOCK2
$$

Answer:

At least <blank>21</blank> of the households have 2 to 6 pets.