The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 7.8 ounces and standard deviation 0.16 ounces.

(a) What is the probability that the average weight of a bar in a Simple Random Sample (SRS) with three of these chocolate bars is between 7.62 and 8 ounces?
ANSWER:

(b) For a SRS of three of these chocolate bars, what is the level $L$ such that there is a 3% chance that the average weight is less than $L$?
ANSWER: