A factory produces biscuit packs of nominal weight 200g. It is believed that the actual weights of biscuit packs follow a normal distribution with a mean of 197.5g and a standard deviation of 2.5g. Scott loves biscuits, and he brought a sample of 15 packs of biscuits.

a) Calculate the standard error of the mean for these 15 packs.

b) Find the probability that the weight of a randomly selected pack is between 195g and 202g.

c) Find the probability that the mean weight of packs in the sample is between 195g and 202g.

d) Compare your answers in b) and c). Explain why or why not they are different.

e) Suppose Scott has found that the mean weight of biscuit packs in the sample is indeed in the interval between 195g and 202g. Is it an indication that this machine needs to be reset for the biscuits manufacturing process? Explain your answer.