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Automobiles arrive at the gate of the student parking structure on a saturday morning at the rate of 6 per hour. a. what is the probability that there will be no cars arriving from from 8 A.M. to 9 A.M. next Saturday morning b. What is the probability that there will be exactly two cars arriving in a 20 minute period on Saturday morining

Michael
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  • Welcome to MSE! If you show us what you have tried perhaps someone can use your work in a hint or answer. Such hints or answers tend to be more useful. – Jay Mar 03 '14 at 01:41

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For the first, the number $X$ of arrivals in an hour is modelled by the Poisson distribution, parameter $\lambda=6$. Thus $\Pr(X=0)=e^{-6}\frac{6^0}{0!}$, or more simply $e^{-6}$.

Fpr the second, the number $Y$ of arrivals in $20$ minutes (one-third of an hour) has Poisson distribution parameter $\frac{6}{3}$. Now the standard formula gives us $\Pr(Y=2)$.

André Nicolas
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