The average resident of Metro City produces 570 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.
A) Between 360 and 780 pounds
B) Between 430 and 710 pounds
C) Between 500 and 640 pounds
D) Between 290 and 850 pounds

Question

Quizplus · Accepted Answer

Chebyshev's theorem states that for any dataset, regardless of distribution, at least $1 - \frac{1}{k^2}$ of the data values will fall within $k$ standard deviations of the mean. To find the range that contains at least 75% of the data, we set $1 - \frac{1}{k^2} \geq 0.75$. Solving for $k$, we find $k \geq \sqrt{4} = 2$. Therefore, we calculate the range as mean ± 2*standard deviation = 570 ± 2*70 = 570 ± 140, which gives us a range from 430 to 710 pounds.

The Average Resident of Metro City Produces 570 Pounds of Solid