the average college student produces 640 pounds of solid waste each year. if the standard deviation is…

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

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

Answer

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