The Varden Packaging Company has a contract to fill 50-gallon barrels with gasoline for use by the U.S. Army. The machine that Varden uses has an adjustable device that allows the average fill per barrel to be adjusted as desired. However, the actual distribution of fill volume from the machine is known to be normally distributed with a standard deviation equal to 0.5 gallons. The contract that Varden has with the military calls for no more than 2 percent of all barrels to contain less than 49.2 gallons of gasoline. In order to meet this requirement, Varden should set the mean fill to approximately 50.225 gallons.

Question

Quizplus · Accepted Answer

To ensure that no more than 2% of barrels contain less than 49.2 gallons, Varden needs to set the mean fill such that 49.2 gallons is at the 2nd percentile of the normal distribution. Using the z-score for the 2nd percentile (-2.05) and the standard deviation (0.5 gallons), the mean fill should be approximately 50.225 gallons.

The Varden Packaging Company Has a Contract to Fill 50-Gallon