Question

Asked Jun 22, 2019

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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 15 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*.

(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.)

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 dependent.

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

Coughs are a rare occurrence. It is reasonable to assume the events are independent.

(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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Step 1

Given that in any large audience you will hear that 15 coughs per minute. r is the number of coughs in a given time interval.

Coughs are rare occurrence and it is reasonabile to assume that events are independent. Here the variable is number of coughs in a given time interval, so it is good choice to use poisson distribution for probability distribution of r.

Step 2

The variable r has poisson distribution with λ = 15. The probability distribution function is shown below.

The probability that 12 or fewer coughs in a 1-minut...

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