A drive-through car-wash service has one station for washing cars. Cars arrive according to a Poisson process with rate $\lambda = 10$ per hour. If the service time is approximately a fixed value of $4$ minutes, what is the expected wait in queue?
My attempt: On average, one person arrives per $6$ minutes, while the service rate is fixed at $4$ minutes, we infer that on average, nobody arrives would need to wait for service. Thus the expected waiting time in queue is $0$.
My question: Is my thought above correct? Note that we are not given the information about the distribution of the service time.