A person with a cough is a persona non grata on airplanes,elevators, or at the theater. In theaters especially, theirritation level rises with each muffled explosion. According toDr. Brian Carlin, a Pittsburgh pulmonologist, in any large audienceyou'll hear about 18 coughs per minute.
(a) Let r = number of coughs in a given time interval. Explainwhy the Poisson distribution would be a good choice for theprobability distribution of r. Coughs are a common occurrence. Itis reasonable to assume the events are independent. Coughs are acommon occurrence. It is reasonable to assume the events aredependent. Coughs are a rare occurrence. It is reasonable to assumethe events are independent. Coughs are a rare occurrence. It isreasonable to assume the events are dependent.
(b) Find the probability of seven or fewer coughs (in a largeauditorium) in a 1-minute period. (Use 4 decimal places.)
(c) Find the probability of at least eight coughs (in a largeauditorium) in a 28-second period. (Use 4 decimal places.)
