Final Answer:
The effective arrival rate for cars is 5 per hour.
Explanation:
The given question is about the arrival rate of cars at a car wash service facility. Cars arriving for service are distributed according to a Poisson distribution with a mean of 5 per hour. The washing and cleaning time of cars varies exponentially with a mean of 10 minutes per car. The facility cannot handle more than one car at a time and has a total of 5 parking spaces.
To calculate the effective arrival rate, we need to calculate the service rate of the facility. The service rate of the facility is calculated by dividing the service time with the number of parking spaces. The service time is the mean time of 10 minutes per car and the number of parking spaces is 5. Hence, the service rate of the facility is 2 per hour. This means that the facility can serve 2 cars per hour.
The effective arrival rate is the difference between the arrival rate and the service rate. The arrival rate of cars is 5 per hour and the service rate of the facility is 2 per hour. Hence, the difference between the arrival rate and the service rate is 3 per hour. This means that the effective arrival rate for cars is 5 per hour.
Therefore, the effective arrival rate for cars is 5 per hour.