Frito-Lay is one of the world’s largest makers of snack foods. One of the final steps in making products like Cheetos and Doritos is to package the product in sacks or other containers. Suppose Frito-Lay managers set the fill volume on Cheetos to an average volume of 16 ounces. The filling machine is known to fill with a standard deviation of 0.25 ounces with a normal distribution around the mean fill level.

a. What is the probability that a single bag of Cheetos will have a fill volume that exceeds 16.10 ounces?

b. What is the probability that a random sample of 12 bags of Cheetos will have a mean fill volume that exceeds 16.10 ounces?

c. Compare your answers to parts a and b and discuss why they are different.