Government regulations mandate that Belgian chocolate bars sold in packages of .5 kilogram cannot wigh less than .5 kilogram, the specified wight on the package. If regulations are violated, the company is fined. The chocolate machine at the Cote d'Or chocolate company fills packages with a standard deviation of 5 grams regardless of the mean setting. To be sure that government regulations are met, the operator decides to set the mean at 515 grams.

a - To check if the process is in control, the operator plans to take samples where each sample consists of 25 chocolate bars. The average weight of this sample of 25 bars is used to determine 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 chocolate bars will weight less than 500 grams (this is the fraction that would violate government regulations)?

c - Clearly producing an excess average chocolate weight of 15 grams just in order to prevent regulation fines is costly in terms of chocolate "given away for free." Cote d'Or management wants to reduce the average excess weight to 3 grams while staying in line with regulations "practically always." which means 99.87%of the time. In whwhat sense will this require improved process technology? Give an explanation in words as well as a specific numeric answer.