Statistics- What is the number of cars waiting for service in the car wash system
Waiting Line (Queuing) Please show all formulas and work!You are planning a car wash to raise money for a local charity. Your charity is considering purchasing an automatic car wash system. You anticipate the cars arriving in a single line and being serviced by one team of washers. Based on historical data, you believe cars will continue to arrive every 20 minutes, and the team can wash a car in about 15 minutes. Assume that the arrival rates follow a Poisson distribution and the service rates are exponentially distributed.1. What is the number of cars waiting for service in the car wash system?2. What is the average time for the car to wait in the car wash system?3. Whatâs the average number of cars in the queue before the full service?4. Whatâs the average time for the car to wait in the queue before service?5. What the probability of none of the cars in the car wash system?