Suppose a brewery has a filling machine that fills 12-ounce bottles of beer. It is known that the amount of beerpoured by this filling machine follows a normal distribution with a mean of 12.47 ounces and a standarddeviation of 0.04 ounce. The company is interested in reducing the amount of extra beer that is poured into the12 ounce bottles. The company is seeking to identify the highest 1.5% of the fill amounts poured by thismachine. For what fill amount are they searching? Round to the nearest thousandth.
A) 12.557 oz
B) 11.913 oz
C) 12.383 oz
D) 12.087 oz

Question

Quizplus · Accepted Answer

To find the fill amount corresponding to the highest 1.5% of fill amounts, we use the z-score associated with the top 1.5% of a normal distribution. Looking up the z-score for the top 1.5%, we find it is approximately 2.17. Using the formula for converting z-scores to raw scores in a normal distribution, $X = \mu + Z\sigma$, where $\mu = 12.47$ ounces is the mean, $\sigma = 0.04$ ounce is the standard deviation, and $Z = 2.17$ is the z-score, we calculate the fill amount as $X = 12.47 + (2.17)(0.04) = 12.47 + 0.0868 = 12.5568$ ounces, which rounds to 12.557 ounces.

Suppose a Brewery Has a Filling Machine That Fills 12-Ounce