Final answer:
The question requires use of queueing theory to calculate the average wait time in a line for a car wash where cars arrive according to a Poisson process. The arrival rate is one car every 6 minutes, against a constant service time of 3 minutes per car. An exact answer cannot be provided without additional details and queuing theory formulas.
Step-by-step explanation:
The question involves calculating the average wait time in a queue system where arrivals follow a Poisson distribution, and service times are constant. Given the arrival rate of 10 autos per hour, we know that on average, there is one arrival every 6 minutes, since there are 60 minutes in an hour (60 minutes ÷ 10 autos = 6 minutes per auto). For a car wash with a constant service time of 3 minutes, we can use these figures to calculate the average waiting time in the queue.
However, to accurately calculate the average wait time in line, we would typically use queueing theory formulas, which are not provided in the question. The data suggests that with an arrival every 6 minutes and a service time of 3 minutes, the system might not be overly congested. Without the appropriate formula or further details on the queuing discipline and the capacity of the system (i.e., number of service channels), we cannot provide an exact value for the average wait time.