After being cut by a special saw, suppose the length of aluminum alloy billets, X, is normally distributed with mean = 96.2 inches and standard deviation = 0.2 inches. Suppose you randomly select 20 billets (assume independence).

1. (a)Determine the probability that exactly 2 are longer than 96.5 inches. Hint: First find the probability that a single billet is longer than 96.5 inches, then use the binomial distribution.
2. (b)Determine the probability that 19 or fewer are have a length less than 96.5 inches.
3. (c)Determine the probability that all 20 billets are between 96.0 and 96.5 inches.