An operator handles adjustments for a group of 8 machines. Adjustment time is exponentially distributed and has a mean of 12 minutes per machine. The machines operate for an average of 85 minutes between adjustments. While running, each machine can turn out 55 pieces per hour. Now find:

a. Average downtime. (1.25 Marks)

b. The probability that a machine will have to wait for an adjustment. (1.25 Marks)