The people staffing the ticket booth at an aquarium are able to distribute tickets and brochures to 440 patrons every hour, according to an exponential distribution. On a typical day, an average of 352 people arrive every hour to gain entrance to the aquarium. The arrivals have been found to follow a Poisson distribution. The aquarium's manager wants to make the arrival process as convenient as possible for the patrons and so wishes to examine several queue operating characteristics.
(a) Find the average number of patrons waiting in line to purchase tickets.
(b) What percentage of the time is the ticket window busy?
(c) What is the average time that a visitor to the aquarium spends in the system?
(d) What is the average time spent waiting in line to get to the ticket window?
(e) What is the probability that there are more than two people in the system? More than three people? (f) What is the probability that there are more than two people in line? More than three people?