A company produces breakfast cereal. The true mean weight of the contents of boxes of its cereal is 20 ounces, and the standard deviation is .6 ounce. The population distribution of weights is normal. Suppose that you purchase four boxes, which can be regarded as a ran- dom sample of all those produced.

(a) What is the standard error of the sample mean weight?

(b) What is the probability that, on average, the contents of these four boxes will weigh less than 19.7 ounces?

(c) What is the probability that, on average, the contents of these four boxes will weigh more than 20.6 ounces?

(d) What is the probability that, on average, the contents of these four boxes will weigh between 19.5 and 20.5 ounces?

(e) Two of the four boxes are chosen at random. What is the probability that, on average. the contents of these two boxes will weigh between 19.5 and 20.5 ounces?