Suppose that a study conducted by the Department of Homeland Security discovered that the average time it took passengers to go through the customs process for international flights arriving at the Atlanta airport was 33 minutes. Assuming that the wait times are distributed according to a Poisson distribution, please answer the following;
a. What is the probability that a passenger gets through customs in more than 45 minutes?
b. What is the probability that a passenger gets through customs in less than 20 minutes?
c. What is the probability that a passenger gets through customs between 30 and 35 minutes?