TP%238_f08 - CE 3102 Fall 2008 Thought Problem 8 Rare...

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CE 3102 Fall 2008 Thought Problem 8 Rare Events A 1-mile long section of rural highway has experienced 6 traffic crashes in the last 5 years. If statewide the probability a vehicle crashes while traversing a 1-mile section of rural highway is 2.0x10 -6 , if the highway section in question has an average daily traffic volume of 1000 vehicles/day, and if vehicle crashes are independent of each other, is this observed crash frequency high enough that we should consider this section atypically dangerous?
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CE 3102 Fall 2008 Though Problem 8 Instructor’s Partial Solution Informally, if the road section of interest has an individual crash probability similar to that of other roads, we can use that probability to compute a probability distribution over the number of crashes occurring in five years. If the observed crash count is improbably large, i.e. if it falls in the right-hand tail of this distribution, we can conclude that there is something different about this road section. If the daily traffic is 1000 vehicles/day, then over 5 years we would expect (5 years)(1000 vehicles/day)(365 days/year) = 1,825,000 vehicles in 5 years. Let X denote the random variable giving the 5-year crash count on our road section. Each of the vehicles using the road has a probability p=2.0x10 -6 of crashing, so we could
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TP%238_f08 - CE 3102 Fall 2008 Thought Problem 8 Rare...

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