Question

vehicles pass through a junction on a busy road at an average rate of 5 per minute.What is the probability that no car will pass in a given minute

Answer 1

The passage time is a Poisson process with mean 5.

$P(0)=\frac{e^{-5}\times{5^0}}{0!}=e^{-5}=0.006737947$

For this purpose the Excel function POISSON.DIST can be used. The formula is given by =POISSON.DIST(0,5,FALSE) which yields 0.006737947.