A person with a cough is apersona non grataon 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 about7coughs per minute.

(a) Letr= number of coughs in a given time interval. Explain why the Poisson distribution would be a good choice for the probability distribution ofr.

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

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

(b) Find the probability ofsixor fewer coughs (in a large auditorium) in a 1-minute period. (Use 4 decimal places.)

(c) Find the probability of at leastsevencoughs (in a large auditorium) in a36-second period. (Use 4 decimal places.)