Much of Trail Ridge Road in Rocky Mountain National Park is over12,000 feet high. Although it is a beautiful drive in summermonths, in winter the road is closed because of severe weatherconditions. Sustained gale-force winds (over 32 miles per hour andoften over 90 miles per hour) occur on the average of 0.7 timesevery 56 hours at a Trail Ridge Road weather station.

(a) Let r = frequency with which gale-force winds occurin a given time interval. Explain why the Poisson probabilitydistribution would be a good choice for the random variabler.

1) Frequency of gale-force winds is a common occurrence. It isreasonable to assume the events are independent.

2) Frequency of gale-force winds is a rare occurrence. It isreasonable to assume the events are dependent.  

3) Frequency of gale-force winds is a common occurrence. It isreasonable to assume the events are dependent.

4) Frequency of gale-force winds is a rare occurrence. It isreasonable to assume the events are independent.

(b) For an interval of 106 hours, what are the probabilities thatr = 2, 3, and 4? What is the probability that r< 2? (Use 2 decimal places for λ. Use 4 decimal placesfor your answers.)

P(2)	 Â
P(3)
P(4)
P(r < 2)

(c) For an interval of 173 hours, what are the probabilities thatr = 3, 4, and 5? What is the probability that r< 3? (Use 2 decimal places for λ. Use 4 decimal placesfor your answers.)

P(3)
P(4)
P(5)
P(r < 3)	 Â