SOLUTION: Cars arrive at a toll both according to a Poisson process with mean 80 cars per hour. If the attendant makes a one-minute phone call, what is the probability that at least 1 car ar

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: Cars arrive at a toll both according to a Poisson process with mean 80 cars per hour. If the attendant makes a one-minute phone call, what is the probability that at least 1 car ar      Log On

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Question 328768: Cars arrive at a toll both according to a Poisson process with mean 80 cars per hour. If the attendant makes a one-minute phone call, what is the probability that at least 1 car arrives during the call?
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
X=number of car passing in an interval of time
X~Poisson (mean=80/hour) or Poisson (mean 80/60min=4/3min)
P%28X=x%29=+mean%5E%28x%29%2Ae%5E%28-mean%29%2Fx%21+ where x>=0)
P%28X=x%29=+%284%2F3%29%5Ex+%2Ae%5E%28-4%2F3%29%2Fx%21


P(at least one car)= 1- P(no cars passing in the interval of interest)
P(X>=1)= 1-P(X=0) = 1+-+e%5E%28-4%2F3%29 = 1-0.264=0.736