A general-purpose auto-repair garage has one mechanic who specializes in muffler installations. Customers seeking service arrive at an average rate of 2 per hour, with a Poisson distribution. The average time to install a muffler is 20 minutes, with negative exponential distribution.
a. On arrival at the garage, how many customers should one expect to find in the system?
b. The management is interested in adding another mechanic when the customer's average time in the system exceeds 90 minutes. If business continues to increase, at what arrival rate per hour will an additional mechanic be needed?