# Poisson Distribution

#### luis0426

##### New Member
On average, every six minutes a car passes by a sector in which it plans to build a tunnel. The passage of many vehicles indicate risk of congestion in the new construction. The engineers in charge of the project need to determine whether the probability that in one hour more than 5 vehicles that circulate by the sector is less than 0.04.

Im stuck, i have that 1 car every 6 minutes ---> 10 cars an hour ----> λ=10, my problem lies in the probability that in one hour more than 5 vehicles that circulate by the sector is less than 0.04, how does the 5 factor in here, I know that P(x=0.4,λ), how does the 5 factor in the problem.

#### BGM

##### TS Contributor
From the previous post, it is glad to know that you know the expected number of car passes in an hour, and also know that this is the new rate for calculation which is a crucial property of Poisson process.

It seems that you claim you know how to calculate the pmf, like $$\Pr\{X = 4\}$$, but do not know how to calculate $$\Pr\{X > 5\}$$

One usual trick for these discrete distribution is that

$$\Pr\{X > 5\} = 1 - \Pr\{X \leq 5\} = 1 - \sum_{x=0}^5 \Pr\{X = x\}$$