A candy manufacturer is marketing a gift box containing four cream-filled nuggets and five pieces of fudge. The manufacturing process for each candy is designed so that the mean weight of a cream-filled nugget is 3 ounces with a standard deviation of 0.2 ounces and the mean weight ofa piece of fudge is 4 ounces with a standard deviation of 0.3 ounces. The boxes have a mean weight of 3 ounces with a standard deviation of 0. I ounce.

(a) Assuming that the weights of the boxes, nuggets, and fudge are independent, what is the mean and

standard deviation of the weight of the box of candy?

(b) Assuming that the weights of the boxes, the nuggets, and the fudge are approximately normally

distributed, what is the probability that a randomly selected box of candy will weigh less than 34

ounces?

(c) If three boxes are selected at random, what is the-probability that at least one of the boxes will weigh

less than 34 ounces?

(d) Determine the probability that a random sample of three boxes will have a mean weight of less than 34

ounces.