Question

A person with a cough is a persona non grata on airplanes, elevators, or at the theater. In theaters especially, the irritation level rises with each muffled explosion. According to Dr. Brian Carlin, a Pittsburgh pulmonologist, in any large audience you'll hear about 15 coughs per minute.

(a) Let r = number of coughs in a given time interval. Explain why the Poisson distribution would be a good choice for the probability distribution of r.
Coughs are a common occurrence. It is reasonable to assume the events are dependent.
Coughs are a rare occurrence. It is reasonable to assume the events are dependent.    
Coughs are a common occurrence. It is reasonable to assume the events are independent.
Coughs are a rare occurrence. It is reasonable to assume the events are independent.


(b) Find the probability of twelve or fewer coughs (in a large auditorium) in a 1-minute period. (Use 4 decimal places.)
 

(c) Find the probability of at least nine coughs (in a large auditorium) in a 32-second period. (Use 4 decimal places.)
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