A shipment of cereal boxes is delivered to a supermarket in Florida. The manager is told that the weights of the cereal boxes are normally distributed, with a mean of 165g and a standard deviation of 5g.

a.Find the probability that a random sample of 200 boxes has a mean weight between 164.9 and 165.1

b.Do I need to state that the distribution of the weights of the cereal boxes is normal in order to do part "a"? Explain in one sentence.