Please help with the question below

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 8 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 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. O Coughs are a rare 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 eight coughs (in a large auditorium) in a 24-second period. (Use 4 decimal places.)