The amount of fill in a half-liter (500 ml) soft drink bottle is normally distributed. The process

Question:

The amount of fill in a half-liter (500 ml) soft drink bottle is normally distributed. The process has a standard deviation of 5 ml. The mean is adjustable.
(a) Where should the mean be set to ensure a 95 percent probability that a half-liter bottle will not be under filled?
(b) A 99 percent probability?
(c) A 99.9 percent probability? Explain.