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A certain supplement advertises 250 mg of vitamin C per pill, although the actual amount varies...

A certain supplement advertises 250 mg of vitamin C per pill, although the actual amount varies slightly according to a normal distribution with a mean of 250 mg and standard deviation of 1.5 mg.

a)What proportion of pills have between 249 and 251 mg of vitamin C?
b)Suppose you take a pill daily for 14 days. What is the probability that on average you receive between 249 and 251 mg of vitamin C?
c)Was it necessary to use the Central Limit Theorem to answer part b? Why or why not?

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