# poisson probability distribution

• March 9th 2008, 08:16 PM
jobear
poisson probability distribution
Im not quite sure about this can someone please give me a hint? Cars arriving for gasoline at a shell station follow a poisson distribution with a mean of 5 per hour. what is the probability that over the next hour only one car will arrive.
• March 9th 2008, 10:33 PM
mr fantastic
Quote:

Originally Posted by jobear
Im not quite sure about this can someone please give me a hint? Cars arriving for gasoline at a shell station follow a poisson distribution with a mean of 5 per hour. what is the probability that over the next hour only one car will arrive.

Let X be the random variable number of cars arriving in one hour.

Substitute $\mu = 5$ into the Poisson formula:

$\Pr(X = x) = \frac{e^{-5} \, 5^x}{x!}$.

You want Pr(X = 1).