A soda-filling machine is intended to dispense 12 ounces of product per can. The actual machine performance has mean value of 12.4 ounces with standard deviation of 0.2 ounces. Based on this information determine:
a) The upper and lower limits (symmetric about the mean fill mass) that includes 99% of all cans,
b) If the mean fill mass can be easily adjusted without changing standard deviation, what mean fill mass must be set to ensure 99.9% of all cans have more than 12 ounces.