1. The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.
Suppose the amount of cereal a manufacturer puts in the boxes is a random variable with a mean of 16.2 ounces and standard deviation of 0.1 ounces. What’s the probability that the box contains more than 13 ounces after you pour yourself a small and a large bowl of cereal out of that box?
2. American Eagle Airlines regularly overbooks its flights. It assumes that on average, five percent of tickets holders do not show up for a flight (they are called no-shows). Its jets have a capacity of 250 and it regularly sells 260 tickets for a flight. What is the probability that there will not be enough seats on a flight?
3. A recent study found that about 40% of Americans are deficient in vitamin D.
a. A random group of 6 Americans is tested and are found to not be deficient in vitamin D. What is the probability that the 7th American is found to be deficient?
b. If 300 are tested, what is the probability that no more than 50 (one-sixth) will have a vitamin D deficiency?
c. What is the probability that none of the first 10 tested will show a vitamin D deficiency?