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 once every 65 hours at a Trail Ridge Road weather station. (a) Letr = 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. O Frequency of gale-force winds is a common occurrence. It is reasonable to assume the events are dependent. O Frequency of gale-force winds is a common occurrence. It is reasonable to assume the events are independent. O Frequency of gale-force winds is a rare occurrence. It is reasonable to assume the events are dependent. O Frequency of gale-force winds is a rare occurrence. It is reasonable to assume the events are independent. (b) For an interval of 104 hours, what are the probabilities that r= 2, 3, and 4? What is the probability that r< 2? (Use two decimal places for 2. Round your answers to four decimal places.) P(2) P(3) P(4) P(r <2) (c) For an interval of 195 hours, what are the probabilities that r= 3, 4, and 5? What is the probability that r<3? (Use two decimal places for 2. Round your answers to four decimal places.) P(3) P(4) P(5) P(r <3)
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 once every 65 hours at a Trail Ridge Road weather station. (a) Letr = 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. O Frequency of gale-force winds is a common occurrence. It is reasonable to assume the events are dependent. O Frequency of gale-force winds is a common occurrence. It is reasonable to assume the events are independent. O Frequency of gale-force winds is a rare occurrence. It is reasonable to assume the events are dependent. O Frequency of gale-force winds is a rare occurrence. It is reasonable to assume the events are independent. (b) For an interval of 104 hours, what are the probabilities that r= 2, 3, and 4? What is the probability that r< 2? (Use two decimal places for 2. Round your answers to four decimal places.) P(2) P(3) P(4) P(r <2) (c) For an interval of 195 hours, what are the probabilities that r= 3, 4, and 5? What is the probability that r<3? (Use two decimal places for 2. Round your answers to four decimal places.) P(3) P(4) P(5) P(r <3)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text: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 once every 65 hours at a Trail Ridge Road weather station.
(a) Letr = 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.
O Frequency of gale-force winds is a common occurrence. It is reasonable to assume the events are dependent.
O Frequency of gale-force winds is a common occurrence. It is reasonable to assume the events are independent.
O Frequency of gale-force winds is a rare occurrence. It is reasonable to assume the events are dependent.
O Frequency of gale-force winds is a rare occurrence. It is reasonable to assume the events are independent.
(b) For an interval of 104 hours, what are the probabilities that r = 2, 3, and 4? What is the probability that r < 2? (Use two decimal places for 2. Round your answers to four decimal places.)
P(2)
P(3)
P(4)
P(r < 2)
(c) For an interval of 195 hours, what are the probabilities that r = 3, 4, and 5? What is the probability that r < 3? (Use two decimal places for 2. Round your answers to four decimal places.)
P(3)
P(4)
P(5)
P(r <3)
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