A company claims that its low-fat yogurt contains only 3 g of fat per cup on average. An independent company randomly selects a cup of the yogurt, which turns out to contain 3.5 g of fat.
a. Assuming the fat levels per cup of the yogurt are approximately normally distributed with mean 3 g and standard deviation 0.2 g, find the probability that a randomly selected cup of the yogurt would have at least 3.5 g of fat.
b. If the assumptions you made in part (a) are true, is the cup containing 3.5 g of fat an unusual event?
c. Describe a scenario in which the cup containing 3.5 g of fat is not an unusual event.
d. On the basis of the cup containing 3.5 g of fat, do the assumptions you made in part (a) seem reasonable? Should a more thorough investigation occur?