Question

the average college student produces 640 pounds of solid waste each year. if the standard deviation is approximately 85 pounds, within what weight limits will at least 88.89% of all students garbage lie? askcuddy between 470 and 810 pounds between 300 and 980 pounds between 385 and 895 pounds between 555 and 725 pounds

Explanation:

Step1: Recall Chebyshev's theorem

Chebyshev's theorem states that for any data set, at least $1-\frac{1}{k^{2}}$ of the data lies within $k$ standard - deviations of the mean. We are given that $1-\frac{1}{k^{2}} = 0.8889$.

Step2: Solve for $k$

\[

$$\begin{align*} 1-\frac{1}{k^{2}}&=0.8889\\ \frac{1}{k^{2}}&=1 - 0.8889\\ \frac{1}{k^{2}}&=0.1111\\ k^{2}&=\frac{1}{0.1111}\approx9\\ k& = 3 \end{align*}$$

\]

Step3: Calculate the lower and upper limits

The mean $\mu = 640$ pounds and the standard deviation $\sigma=85$ pounds.
The lower limit is $\mu - k\sigma=640-3\times85=640 - 255 = 385$ pounds.
The upper limit is $\mu + k\sigma=640+3\times85=640 + 255 = 895$ pounds.

Answer:

Between 385 and 895 pounds