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

correct answer:
the answer is 7181.

explanation:
thus, approximately 88.89% of the students will produce waste between 508.25 and 771.75 pounds.
the possible answers provided do not seem to directly

between 470 and 810 pounds

between 300 and 980 pounds

between 385 and 895 pounds

between 555 and 725 pounds

Explanation:

Step1: Identify the z - score

Since at least 88.89% of the data lies within a certain range, the proportion of data outside the range is \(1 - 0.8889=0.1111\). Dividing this by 2 (for both tails), we get \(0.05555\) for each tail. Looking up in the standard - normal table, the z - score corresponding to a right - tail area of \(0.05555\) is approximately \(z = 1.5\).

Step2: Calculate the lower limit

The formula for the lower limit \(L\) of a normal distribution is \(L=\mu - z\sigma\), where \(\mu = 640\) (mean) and \(\sigma = 85\) (standard deviation). So \(L=640-1.5\times85=640 - 127.5 = 512.5\) pounds.

Step3: Calculate the upper limit

The formula for the upper limit \(U\) of a normal distribution is \(U=\mu + z\sigma\). So \(U=640 + 1.5\times85=640+127.5 = 767.5\) pounds.

Answer:

Between 512.5 and 767.5 pounds