SOLUTION: The transportation manager for the State of New Jersey has determined that the time between arrivals at a toll booth on the state’s turnpike is exponentially distributed with λ
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Question 666197: The transportation manager for the State of New Jersey has determined that the time between arrivals at a toll booth on the state’s turnpike is exponentially distributed with λ = 4 cars per minute. Based on this information, what is the probability that the time between any two cars arriving will exceed 11 seconds? Answer by swincher4391(1107) (Show Source):
You can put this solution on YOUR website! λ = 4/60 cars per second so the cdf of the exponential is 1-e^-λ*t
So P[t<=11] = 1 - e^(-11*(4/60)) = 1-e^(-0.733333).
Then P[t>11] = 1-P[t<=11] = 1 - (1-e^-0.73333) = e^-0.73333 = .4803
