By law, a box of cereal labeled as containing 18 ounces must contain at least 18 ounces of cereal. The machine filling the boxes produces a distribution of fill weights with a mean equal to the setting on the machine and with a standard deviation equal to 0.03 ounce. To ensure that most of the boxes contain at least 18 ounces, the machine is set so that the mean fill per box is 18.09 ounces. Assuming nothing is known about the shape of the distribution, what can be said about the proportion of cereal boxes that contain less than 18 ounces.
A) The proportion is at most 11%.
B) The proportion is at least 89%.
C) The proportion is at most 5.5%.
D) The proportion is less than 2.5%.

Question

Quizplus · Accepted Answer

Using Chebyshev's inequality, at least 89% of the boxes will contain between 18.03 and 18.15 ounces, meaning at most 11% contain less than 18 ounces.

By Law, a Box of Cereal Labeled as Containing 18