Consider a manufacturing situation involving the use of six robots. There is one robot attendant who changes end-of-arm tooling for the robots, programs the robots, and performs setup changes for the robots. The time between requirements for an attendant for an individual robot is exponentially distributed with an average value of 2 hours.

The time required to tend to the robot is also exponentially distributed and has an average value of 0.40 hour.

a. What is the probability of an idle attendant?

b. Determine the average number of robots waiting on the attendant to begin performing a service.