Question

A company that manufactures and bottles apple juice has a machine that automatically fills 16-ounce bottles. There is some variation in the exact amount of juice dispensed into each bottle. If the amount of liquid per bottle can be assumed to have a normal distribution, find the percentage of bottles that will either be overfilled or underfilled by at least 0.5 ounce.

A) 30.85%
B) 38.30%
C) 61.70%

Answer 1

To determine the percentage of apple juice bottles either overfilled or underfilled by at least 0.5 ounces, we need to calculate the z-scores for these deviations and find the corresponding areas under a normal distribution curve.

Step-by-step explanation:

The question concerns a company bottling apple juice and the variation in the amount of juice dispensed into each bottle, which follows a normal distribution. To find the percentage of bottles that will be overfilled or underfilled by at least 0.5 ounces, we need to look at the tails of the normal distribution curve. Without the standard deviation and the mean of the process, a general solution cannot be provided.

However, in the context of a normal distribution, these tails represent the portions of the curve that fall more than a certain number of standard deviations away from the mean. If we knew the standard deviation, we could calculate the z-scores corresponding to being 0.5 ounces away from the mean (which would be the mean minus 0.5 ounces and the mean plus 0.5 ounces, respectively). Then, we would consult a standard normal distribution table (or use software/calculator) to find the area under the curve beyond these z-scores. This area represents the percentage of bottles overfilled or underfilled by at least 0.5 ounces.