The amount of cereal dispensed into "16-ounce" boxes of Captain Crisp cereal was normally distributed with mean 16.12 ounces and standard deviation 0.20 ounces. (Use TI-84 calculator.)

a) (1.5pts) A box of Captain Crisp is considered "underfilled" if it has less than 16 ounces. What proportion of boxes are "underfilled"?

b) (1.5pts) Find the probability that exactly 2 out of 9 randomly and independently selected boxes of cereal contain less than 16 ounces.

c) (1.5pts) Find the probability that the sample mean amount of cereal for a random sample of 9 boxes is less than 16 ounces.

d) (2pts) Suppose that the machine can be adjusted to change the mean while the standard deviation remains at 0.20 ounces. What must the mean be so that only 20% of all the boxes are "underfilled"? (Hint: You have an x-value, Q , and can find a z-score. How can you find M ?)

e) (1.5pts) Quality control at Admiral Mills oversees the production of Captain Crisp cereal. A shipment of 64 boxes of Captain Crisp has been returned to the company with the complaint that the average amount of cereal in the 64 boxes is in at the 10th percentile (of all possible averages from 64 box shipments) and this average is unacceptably low. What is the average amount of cereal in the 64 boxes?