Calculate the probability of x amount of cars arriving at an intersection each minute.

Question

We know that about 400 cars arrive at an intersection each hour, from one of the four roads, and we would like to know the probability that over the next minute x, y, z, h and k amount of cars will arrive at the intersection from this road.

For example in an interval of 5 cars from 0 cars to 20 cars a minute:

x = 0

z = 5

y = 10

h = 15

k = 20

If possible how would we go about calculating this or come up with an okay estimation?

Edit:

We have currently tried using the formular: $\frac{CarsEachHour}{x * 60 min/hour}$ which seems to kinda work for one case, but extending it to a total of 5 cases seems hard.

Answer 1

You can use Poisson Distribution with $\lambda = \frac{400}{60} = \frac{20}{3}$

For example x = 5 cars per minute

$P(X = 5) = \dfrac{e^{-\frac{20}{3}}.(\frac{20}{3})^5}{5!}$

The table below gives all the probabilities