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.

*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*.

(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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