A company claims that its cheddar cheese contains 3.5 g of fat per serving on average. An independent company randomly selects a package of the cheese, which turns out to contain 3.8 g of fat per serving.
a. Assuming the fat levels per serving of the cheese are approximately normally distributed with mean 3.5 g and standard deviation 0.12 g, find the probability that a randomly selected package of cheese would have at least 3.8 g of fat per serving.
b. If the assumptions you made in part (a) are true, is the package containing 3.8 g of fat per serving an unusual event?
c. Describe a scenario in which the package containing 3.8 g of fiber per serving is not an unusual event.
d. On the basis of the package containing 3.8 g of fiber per serving, do the assumptions you made in part (a) seem reasonable? Should a more thorough investigation occur?