1. A service that repairs air conditioners sells maintenance agreements for $80 a year. The average cost for repairing an air conditioner is $350. If 1% of all people who purchase these maintenance agreements have air conditioners that require repair, then what is the service's expected profit per maintenance agreement?
2. Look back at problem #3. Suppose the service is able to sell 2000 such policies over the year. What is their total expected profit on these 2000 policies? Your answer must be based on your response to problem #3 in order to receive full credit.
3. The percentage of the population who like olives is 62%. Suppose 30 people are chosen at random. What is the probability that exactly 16 of them like olives? You must show your work using a calculator function to receive credit.
4. Approximately 55% of high school students participate in athletic programs. If we choose 5 high school students at random, what is the probability that at least one of them participates in an athletic program? You must show your work using a calculator function to receive credit.
5. You take a multiple choice test that you are not prepared for, so you have to guess on all twenty questions. The probability that you guess correctly on any given question is 20% (since there are five choices on each question). What is the probability that you are able to guess ten or more correct answers? You must show your work using a calculator function to receive credit.
6. When someone buys a ticket for an airline flight, there is a 0.0995 probability that the person will not show up for the flight. An agent for Air America wants to book 24 people on an airplane that can seat only 22. If 24 people are booked, find the probability that not enough seats will be available. You must show your work using a calculator function to receive credit.
7. According to the website correlated.org, 41% of people are okay with eating spray cheese from a can. Suppose we consider all possible samples of 200 people. Find the mean and standard deviation for the random variable "number of people who are okay with eating spray cheese from a can" for groups of this size.