The article "Probabilistic Risk Assessment of Infrastructure Networks Subjected to Hurricanes"t suggests a uniform distribution as a model for the actual landfall position of the eye of a hurricane. Consider the random variable x = distance of actual landfall from predicted landfall. Suppose that a uniform distribution on the interval that ranges from 0 km to 400 km is a reasonable model for x. (a) What is the probability that x is at most 300? (b) What is the probability that x is between 300 and 450? (c) What is the probability that x is between 150 and 300? (d) Explain why the probabilities calculated in parts (b) and (c) are equal.
The article "Probabilistic Risk Assessment of Infrastructure Networks Subjected to Hurricanes"t suggests a uniform distribution as a model for the actual landfall position of the eye of a hurricane. Consider the random variable x = distance of actual landfall from predicted landfall. Suppose that a uniform distribution on the interval that ranges from 0 km to 400 km is a reasonable model for x. (a) What is the probability that x is at most 300? (b) What is the probability that x is between 300 and 450? (c) What is the probability that x is between 150 and 300? (d) Explain why the probabilities calculated in parts (b) and (c) are equal.
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![= 0.0025, and the probability of interest was determined to be P(xs 300). The distribution curve is
400
The height of the distribution curve was determined to be
as follows.
0.0030
0.0025
0.0020
0.0015
0.0010
0.0005
0.0000
100
200
300
400
The probability
Since the distribution is valid only for x values between 0 and 400, the rectangle representing P(x s 300) will have a base length of
0.0025.
of the event that x is at most 300 will be the area of the rectangle with this base and height
Substitute these values to find the desired probability.
P(x s 300) = (base)(height)
)(0.0025)
Density](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea34878c-1379-4c59-af86-09d7e592a5f8%2F86dd3551-b76e-42da-9535-8c504aabce37%2F6ni9dlm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:= 0.0025, and the probability of interest was determined to be P(xs 300). The distribution curve is
400
The height of the distribution curve was determined to be
as follows.
0.0030
0.0025
0.0020
0.0015
0.0010
0.0005
0.0000
100
200
300
400
The probability
Since the distribution is valid only for x values between 0 and 400, the rectangle representing P(x s 300) will have a base length of
0.0025.
of the event that x is at most 300 will be the area of the rectangle with this base and height
Substitute these values to find the desired probability.
P(x s 300) = (base)(height)
)(0.0025)
Density
![The article "Probabilistic Risk Assessment of Infrastructure Networks Subjected to Hurricanes"t suggests a uniform distribution as a model for the actual landfall
position of the eye of a hurricane. Consider the random variable x = distance of actual landfall from predicted landfall. Suppose that a uniform distribution on the
interval that ranges from 0 km to 400 km is a reasonable model for x.
(a) What is the probability that x is at most 300?
(b) What is the probability that x is between 300 and 450?
(c) What is the probability that x is between 150 and 300?
(d) Explain why the probabilities calculated in parts (b) and (c) are equal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea34878c-1379-4c59-af86-09d7e592a5f8%2F86dd3551-b76e-42da-9535-8c504aabce37%2F76oecgh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The article "Probabilistic Risk Assessment of Infrastructure Networks Subjected to Hurricanes"t suggests a uniform distribution as a model for the actual landfall
position of the eye of a hurricane. Consider the random variable x = distance of actual landfall from predicted landfall. Suppose that a uniform distribution on the
interval that ranges from 0 km to 400 km is a reasonable model for x.
(a) What is the probability that x is at most 300?
(b) What is the probability that x is between 300 and 450?
(c) What is the probability that x is between 150 and 300?
(d) Explain why the probabilities calculated in parts (b) and (c) are equal.
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