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 12 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 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.     Coughs are a rare occurrence. It is reasonable to assume the events are dependent.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 eight coughs (in a large auditorium) in a 33-second period. (Use 4 decimal places.)

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.