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 about15coughs per minute.

(a) Letr= number of coughs in a given time interval.

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

(c) Find the probability of at leastfivecoughs (in a large auditorium) in a20-second period. (Use 4 decimal places.)