15.     A cereal manufacturer claims that the gross weight (including packaging) of a box of cereal labeled as weighing 12 oz has a mean of 12.2 oz and a standard deviation of 0.1 oz. You gather 75 boxes and weigh them all together. Let S denote the total weight of the 75 boxes of cereal.

a.    If the claim is true, what is P(S ≤ 914.8)?

b.    Based on the answer to part (a), if the claim is true, is 914.8 oz an unusually small total weight for a sample of 75 boxes?

c.    If the total weight of the boxes were 914.8 oz, would you be convinced that the claim was false? Explain.

d.    If the claim is true, what is P(S ≤ 910.3)?

e.    Based on the answer to part (d), if the claim is true, is 910.3 oz an unusually small total weight for a sample of 75 boxes?

f.    If the total weight of the boxes were 910.3 oz, would you be convinced that the claim was false? Explain.