The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed with a mean of 12.2 fluid ounces and a standard deviation of 0.1 fluid ounce.
a) What is the probability a fill volume is less than 12 fluid ounces? (Round your answer to 4 decimal places.)
b) If all cans less than 12.1 or greater than 12.6 ounces are scrapped, what proportion of cans is scrapped? % (Round your answer to 4 decimal places.)
c) Determine specifications (in ounces) that are symmetric about the mean that include 99% of all cans.