I have to complete the question for a homework task and I'm confused if it is a Poisson or exponential distribution. any insight would be appreciated.
cars arrive at a car wash in a town at an average rate of 50 per hour.
Q: If you arrive within a three minutes of another car , you must wait outside. What is the probability that, when you turn up to vote, must wait outside?
The time between consecutive rivals is exponentially distributed, with a mean of $2$ minutes. It couldn't be Poisson-distributed, as it's continuous. It's at most a minute with probability $1-e^{-1/2}$. What is Poisson-distributed is the number of arrivals per hour, or minute or whatever.