Question

The average resident of Metro City produces 630 pounds of solid waste each year, and the standard deviation is approximately 70 pounds. Use Chebyshev's theorem to find the weight range that contains at least 75% of all residents' annual garbage weights.

Answer 1

Answer:

A garbage weight between 490 pounds and 770 pounds.

Explanation:

The Chebyshev theorem says that at least 75% of the data is within the following interval:

$x^{\prime}-2s\leq x\leq x^{\prime}+2s$

Where x' is the average and s is the standard deviation.

So, replacing x' by 630 pounds and s by 70 pounds, we get that the weight range for the annual garbage weights is:

$\begin{gathered} 630-2(70)\leq x\leq630+2(70) \\ 490\leq x\leq770 \end{gathered}$

Therefore, the weight range that contains at least 75% of all residents' annual is a garbage weight between 490 pounds and 770 pounds.