Question

Cars arrive at the Dariette, a drive through restaurant, at a rate of 15 cars per hour. What is the probability that 10 or fewer cars arrving in the next hour

Answer 1

Probability that 10 or fewer cars arriving in the next hour will be :

$\small P(X\leq 10) = P(X=0)+P(X=1)+P(X=2)+....................+P(X=10)$

$\small P(X=x) =\frac{\lambda^x e^{-\lambda}}{x!}$

We are given , Mean = 15

So,

$\small \lambda = 15$

We can either compute all the terms and then add them up to get the answer or we can simple use the Excel function " POISSON.DIST() " :

$\small P(X\leq 10)=POISSON.DIST(10,15,TRUE) = 0.118464$