Question

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. Sustained gale-force winds (over 32 miles per hour and often over 90 miles per hour) occur on the average of 0.7 times every 56 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.

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

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

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

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

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

P(2)
P(3)
P(4)
P(r < 2)

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

P(3)
P(4)
P(5)
P(r < 3)

Answer 1