2. ABC Store operates with four check-out counters. The manager uses the following schedule to determine the number of counters in operation, depending on the number of customers in store: No. of customers in store No. of counters in operation 1 to 3 1 4 to 6 2 7 to 8 3 More than 8 4 Suppose that the interarrival time at the checkout area is exponential with mean 5 minutes and that the checkout time per customer is also exponential with mean 10 minutes. Determine the following: (a) The steady-state probabilities, ; for all j. (b) The probability that a fourth counter will be needed. (e) The average number of idle counters