A company claims that its high-protein shake contains 30 g of protein per serving on average. An independent company randomly selects a package of the shake, which turns out to contain 28.6 g of protein per serving.
a. Assuming the protein levels per serving of the shake are approximately normally distributed with mean 30 g and standard deviation 0.5 g, find the probability that a randomly selected package of the shake would have at most 28.6 g of protein per serving.
b. If the assumptions you made in part (a) are true, is the pack- age containing 28.6 g of protein per serving an unusual event?
c. Describe a scenario in which the package containing 28.6 g of protein per serving is not an unusual event.
d. On the basis of the package containing 28.6 g of protein per serving, do the assumptions you made in part (a) seem reasonable? Should a more thorough investigation occur?