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At a local fast-food joint, cars arrive randomly at a rate of 12 every 30 minutes. The fast food joint takes an average of 2 minutes to serve each arrival. The utilization factor for this system is A) 0.467. B) 0.547. C) 0.800. D) 0.133. E) None of the above 4)A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. a) What is the average length of the line? A) 3.429 B) 1.929 C) 1.143 D) 0.643 E) None of the above b) How long does the average person spend waiting for a clerk? A) 3.429 minutes B) 1.929 minutes C) 1.143 minutes D) 0.643 minute E) None of the above c) What proportion of time are both clerks idle? A) 0.643 B) 0.250 C) 0.750 D) 0.143 E) None of the above