When confronted with an in-fight medical emergency, pilots and crew can consult staff physicians at a global response center located in Arizona. If the global response center is called, there is a 4.8 percent chance that the fight will be diverted for an immediate landing. Suppose the response center is called 8,465 times in a given year.
(a) What is the expected number of diversions?
(b) What is the probability of at least 400 diversions?
(c) Fewer than 450 diversions? Show your work carefully.