Much of Trail Ridge Road in Rocky Mountain National Park is over 12,000 feet hig

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 0.8 times every 68 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.

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

(b) For an interval of 112 hours, what are the probabilities that r = 2, 3, and 4? What is the probability that r < 2? (Use 2 decimal places for . Use 4 decimal places for your answers.)

P(2)

P(3)

P(4)

P(r < 2)

(c) For an interval of 179 hours, what are the probabilities that r = 3, 4, and 5? What is the probability that r < 3? (Use 2 decimal places for . Use 4 decimal places for your answers.)

P(3)

P(4)

P(5)

P(r < 3)

P(2)

P(3)

P(4)

P(r < 2)

Explanation / Answer

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 0.8 times every 68 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.

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

(b) For an interval of 112 hours, what are the probabilities that r = 2, 3, and 4? What is the probability that r < 2? (Use 2 decimal places for . Use 4 decimal places for your answers.)

P(2)

P(3)

P(4)

P(r < 2)

(c) For an interval of 179 hours, what are the probabilities that r = 3, 4, and 5? What is the probability that r < 3? (Use 2 decimal places for . Use 4 decimal places for your answers.)

P(3)

P(4)

P(5)

P(r < 3)

P(2)

P(3)

P(4)

P(r < 2)

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