A candy maker produces mints that have label weight of 20 grams on each box. Assume that the weight of a box of mints is normally distributed with a standard deviation of 0.4 grams.
(a) Determine the sampling distribution of sample mean weight for a sample of dozen box of mints?
(b) Suppose you bought a dozen boxes of mints and found the average weight to be 19.7 grams. What is the probability that the sample mean of a dozen boxes of mints will weigh as low as 19.7 grams or lower? Would you consider this as evidence that the candy maker's claim is incorrect? Explain.
(c) Suppose you bought such a box of mints and it weighed 19.7 grams. What is the probability that a box of mints will weigh as low as 19.7 grams or lower? Would you consider this as evidence that the candy maker's claim is incorrect? Explain.