I am stuck on this question, I don't exactly know how to approach it. Thanks for any advice.
The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed. Suppose that the mean of the filling operation can be adjusted easily, but the standard deviation remains at 0.1 ounce.
a) At what value should the mean be set so that 99.9% of all cans exceed 12 ounces?
b) At what value should the mean be set so that 99.9% of all cans exceed 12 ounces if the standard deviation can be reduced to 0.05 fluid ounce?