Chapter 5.5, Problem 4E

Let X equal the weight of the soap in a ‘6-pound box. Assume that the distribution of X is $N\left(6.05,0.0004\right)$.

(a) Find $P\left(X<6.0171\right)$.

(b) If nine boxes of soap are selected at random from the production line, find the probability that at most two boxes weigh less than 6.0171 pounds each. HINT: Let Y equal the number of boxes that weigh less than 6.0171 pounds.

(c) Let $\bar{X}$ be the sample mean of the nine boxes. Find $P\left(\bar{X}\le 6.035\right)$.