The manager of a grocery store in Sunnyville (a retirement community) wants to make sure that senior citizens who shop in her store receive good service. The store has a separate checkout counter for senior citizens. On average, 20 senior citizens per hour arrive at the counter, according to a Poisson distribution, and are served at an average rate of 30 customers per hour, with exponential service times. Find the following operating characteristics: a. Probability of zero customers in the system. b. Average utilization of the senior citizen checkout clerk. c. Average number of customers in the system. d. Average number of customers in line. e. Average time spent in the system. f. Average waiting time in line. g. What service rate would be required if customers averaged only 8 minutes in the system? What are the steps for solving this problem?