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 person with a cough is apersona 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 20 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 rare occurrence. It is reasonable to assume the events are independent.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 dependent.Coughs are a common occurrence. It is reasonable to assume the events are independent.

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

(c) Find the probability of at least twelve coughs (in a large auditorium) in a 27-second period. (Use 4 decimal places.)

Jun 08, 2022

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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,...

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