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. Suppose Varden managers are unwilling to set the mean fill at any level higher than 50 gallons. Given that, in order to meet the requirements, they will need to increase the standard deviation of fill volume.

Question

Quizplus · Accepted Answer

To meet the requirement of no more than 2 percent of all barrels containing less than 49.2 gallons of gasoline, Varden managers would need to adjust the mean fill level closer to 50 gallons, not increase the standard deviation. Increasing the standard deviation would result in a wider spread of the fill volumes, potentially increasing the percentage of barrels with less than 49.2 gallons, which would not help in meeting the contract requirements.

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