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 9 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.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 50E: Flexible Work Hours In a recent survey, people were asked whether they would prefer to work flexible...
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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, a Pittsburgh pulmonologist, in any large audience you'll hear about 9 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

a.Coughs are a common occurrence. It is reasonable to assume the events are dependent.
b.Coughs are a rare occurrence. It is reasonable to assume the events are independent.    
c.Coughs are a rare occurrence. It is reasonable to assume the events are dependent.
d.Coughs are a common occurrence. It is reasonable to assume the events are independent.
 
(b) Find the probability of eleven 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 34-second period. (Use 4 decimal places.)
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