An airline intentionally overbooks its flight because it knows that that probability an individual passenger will not show up is 0.05 (assume passengers are independent). The plane can hold 80 people, and the airline sold 81 tickets for the flight.
a. What is the probability that there will not be enough seats for the passengers who show up to fly?
b. Do you think it is reasonable to assume the passengers are independent! Why or why not?
c. The airline wants to predict their profit from this flight. Each passenger paid $200 for his or her ticket, and if someone does not show up, he or she is refunded only $150 of the ticket purchase price. What are the expected value and the standard deviation of the airline's income from this flight?
d. Using the story from part c, what is a customer's expected cost and the standard deviation of the cost?