Question: A company produces breakfast cereal. The true mean weight of the contents of boxes of its cereals is 20 ounces and the standard deviation is 0.6 ounce. Suppose that you purchase four boxes.

(a) Is it necessary to assume that the weights are normally distributed to use the Central Limit Theorem?

(b) What is the standard error of the sample mean

(c) If the company’s claim is true, what is the probability that you will get a sample mean smaller than 19.7 ounces?

(d) You are not happy with the results and decide to buy 60 boxes more. Repeat all the exercises (a) to (c) with this new sample.