By law, a box of cereal labeled as containing 20 ounces must contain at least 20 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 0.04 ounce. To ensure that most of
The boxes contain at least 20 ounces, the machine is set so that the mean fill per box is 20.12 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 20 ounces.
A)The proportion is at most 11%.
B)The proportion is less than 2.5%.
C)The proportion is at most 5.5%.
D)The proportion is at least 89%.

Question

Quizplus · Accepted Answer

The proportion of cereal boxes that contain less than 20 ounces is at most 11%. This is because the machine is set so that the mean fill per box is 20.12 ounces, and the standard deviation is 0.04 ounce. This means that the distribution of fill weights is approximately normal, and the proportion of boxes that contain less than 20 ounces is equal to the area under the normal curve to the left of 20 ounces. This area is approximately 11%.

By Law, a Box of Cereal Labeled as Containing 20