Billy Joe’s Car Wash (BJCW) just purchased a new automated washing system. With the new machine, (BJCW) can wash an average of 25 cars per hour. The standard deviation of washing times in 2.4 minutes, is due primarily to the different car treatments and manual pre-washing (performed by a team of employees). Billy Joe estimates that customers arrive, on average, every 2.58 minutes and that the inter-arrival times are exponentially distributed (I didn’t know Billy Joe had it in him…).

1. Billy Joe is concerned about customer waiting time. Calculate the expected customer waiting time for the system described.
2. Evaluate this system’s capacity. Is it adequate for the operation? Why/Why not?
3. Billy Joe suspects that the washing times may be exponentially distributed. With the information you have, is he true? Explain the basis for your argument and show your analysis.
4. Billy Joe has heard, from a friend taking Process Analysis and Quality Management at the University of Portland, that “uncertainty = bad”. He has noted that his service times are longer than he’d like and that his service time is uncertain. How would the expected waiting time change if Billy Joe could somehow eliminate all of his service time variability?
5. If eliminating service time variability completely proves impossible, by how much would Billy Joe has to reduce his service time variability (i.e. standard deviation) in order to achieve waiting times of no more than 20 minutes?