15. Theater: Coughs 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 11 coughs per minute

(Source: USA Today).

(a) Let r 5 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 three or fewer coughs (in a large auditorium) in a 1-minute period.

(c) Find the probability of at least three coughs (in a large auditorium) in a 30-second period.