Regulations on milk packaging is such that a gallon of milk cannot...

Regulations on milk packaging is such that a gallon of milk cannot have less than 1 gallon in the container. If this is violated, the company is fined. The company fills milk containers with a standard deviation of 0.5 ounces regardless of the mean setting. To be sure that regulations are met, the operator decides to set the mean at 1 gallon (128 ounces) + 1.5 ounces, or 129.5 ounces.

a. To check if the process is in control, the operator plans to take samples where each sample consists of 4 gallons containers. The average volume of this sample of 4 containers is used to determined if the process is in control. Following industry practice, what control limits should the operator use?

b. If the process is in control, approximately what fraction of contrainers will have a volume under 1 gallon (this is the fraction that would violate government regulation)?

c. Putting more than 1 gallon in a container to prevent regulation fines is costly in terms of milk given away. Management wants to reduce the average excess volume to 1 ounce while staying in line with regulations "practically always," which means 99.87% of the time. In what sense will this require improved process technology? Give an explanation in words as well as a specific numeric answer.