2. Let X denote the amount of soap in a box advertised as a "6 pound box". Assume that

X~ N(6.05, 0.0004).

(a) Find P(X < 6.0171).

(b) If nine boxes are selected at random, find the probability that at most two weigh less

than 6.0171 pounds each.

(c) For the nine boxes, find P(X < 6.0171).

(d) Over several years, a loyal customer buys 90 boxes of the same soap. Find the probability

P(X < 6.045).

TEKO 100