The Powerball lottery is one of the most popular lotteries in the United States. From time to time, the jackpot exceeds $100 million. As a result so many more people buy Powerball tickets that there are frequent lineups at convenience stores. A statistician interviews hundreds of people in queues and asks how many tickets each person intends to buy. He concludes that the number of tickets is a Poisson random variable with a mean of 5.

a. What proportion of people will buy only 1 ticket?

b. What proportion of people will buy 5 or fewer tickets?

c. What proportion of people will buy 8 or more tickets?