(Solved): The amount of fill in a half-liter \( (500 \mathrm{ml}) \) soft drink bottle is normally distribut ...

The amount of fill in a half-liter \( (500 \mathrm{ml}) \) 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 underfilled? (Round your answer to 2 decimal places.) (b) Where should the mean be set to ensure a 99 percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.) (c) Where should the mean be set to ensure a \( 99.9 \) percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.)