A person with a cough is a persona non grata on airplanes, elevators, or at the

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 14 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 dependent.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 independent.Coughs are a common occurrence. It is reasonable to assume the events are independent.

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


(c) Find the probability of at least seven coughs (in a large auditorium) in a 36-second period. (Use 4 decimal places.)

Explanation / Answer

here frequency of cough = 14 coughs per minute

(a) Coughs are a common occurrence. It is reasonable to assume the events are independent. Option D is correct.

(b) If x is the number of coughs per minute in a 1 - minute period.

Pr(x <=6 ; 14) = 0.0142

(c) Pr(x >= 7) = 1 - Pr(x < 7) = 1 - 0.0142 = 0.9858

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