In the previous exercise, suppose that the mean of the filling operation can be adjusted easily, but the standard deviation remains at 0.1 ounce. (Beverage companies can be heavily penalized for selling cans that do not fulfill the stated promise of 12 ounces.)
(a) What is the minimum value that the mean can be set while ensuring that 99.9% of all cans exceed 12 ounces?
(b) What is the minimum value that the mean can be set while ensuring that 99.9% of all cans exceed 12 ounces if the standard deviation can be reduced to 0.05 fluid ounce?