Much of Trail Ridge Road in Rocky Mountain National Park is over 12,000 feet high. Although it is a beautiful drive in summer months, in winter the road is closed because of severe weather conditions. Winter Wind Studies in Rocky Mountain National Park by Glidden (published by Rocky Mountain Nature Association) states that sustained gale-force winds (over 32 miles per hour and often over 90 miles per hour) occur on the average of once every 60 hours at a Trail Ridge Road weather station.

(a) Let r = frequency with which gale-force winds occur in a given time interval. Explain why the Poisson probability distribution would be a good choice for the random variable r.

(b) For an interval of 108 hours, what are the probabilities that r < 2, 3, and 4? What is the probability that r < 2?

(c) For an interval of 180 hours, what are the probabilities that r = 3, 4, and 5? What is the probability that r < 3?