Basset’s Liquid Filler III is a machine that falls containers with a preset amount of semi-liquid product that will be used in its plastics molding process. The average fill weight for the machine can be set and controlled, but there is inevitably some variability in the process. Actual fill-weights, in fact, follow a normal pattern around the mean, with a known standard deviation of .05 ounces.
a. If the machine is set for a mean fill weight of 8 ounces, what proportion of containers will be filled with less than 8 ounces of product?
b. If the machine is set for a mean fill weight of 8.05 ounces, what proportion of the containers will be filled with less than 8 ounces of product?
c. If you want to ensure that no more than 1% of the containers will be filled with less than 8 ounces of product, where should you set the mean fill weight?