y Notes Ask Your Teacher A person with a cough is a persona non grata on airplan

Question

y Notes Ask Your Teacher 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'l 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 O Coughs are a rare occurrence. It is reasonable to assume the events are dependent. O Coughs are a common occurrence. It is reasonable to assume the events are independent. O Coughs are a rare occurrence. It is reasonable to assume the events are independent. O Coughs are a common occurrence. It is reasonable to assume the events are dependent. (b) Find the probability of nine or fewer coughs (in a large auditorium) in a 1-minute period. (Use 4 decimal places.) (c) Find the probability of at least four coughs (in a large auditorium) in a 26-second period. (Use 4 decimal places.)

Explanation / Answer

Coughs are usually common occurrence and it is independent for one another and for the poisson distribution we should have to be selected the events must be a independent events

Also the average cough rate is given with a independent events poisson distribution is the best method to opt

Hence option 2 is correct

P( less than or equal to 9)= (e-uur/r!)

Where r =0,1,....9.

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