A brewery's filling machine is adjusted to fill bottles with the mean of 33 oz. of ale and variance of 0.006. Periodically, a bottle is checked and the amount of ale noted.
a) Supposing the amount of fill is normally distributed, what is the probability that the next randomly checked bottle haves more than 33.10 oz? (Provide your answer correct to four decimal places.)
b) Let's say you buy 101 bottles of this ale for party. How many bottles would you expect to determine containing more than 33.10 oz. of ale? (Round your answer up to the nearest whole number.) bottles