Mr. Sheriff is tracking the cars over the speed limit on I-40. He positions his

Question

Mr. Sheriff is tracking the cars over the speed limit on I-40. He positions his vehicle right behind an overpass. He tries to ticket cars that exceed the speed limit by 10 miles per hour or more. The inter- arrival time between cars exceeding the speed limit by 10 miles per hour is exponentially distributed with a mean of 4 minutes. What is the probability of Mr. Sheriff ticketing a speeding car within the next 5 minutes?

please show all of your work. I am using this as a study aid. if you are writting this out by hand please make sure its legible. thank you <3

Explanation / Answer

Note that for exponentially distributed variables,

P(x<c) = 1 - exp(-c/u)

where u = mean = 4.

Hence, for c = 5,

P(x<5) = 1 - exp(-5/4) = 0.713495203 [ANSWER]

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