Question 3 A In a single pump petrol station, it was observed that the inter-arrival times and service times are as given in the table. Inter-arrival time Service time Minutes Probability Minutes Probability 1 0.10 2 0.10 3 0.17 4 0.23 5 0.35 6 0.35 7 0.23 8 0.22 9 0.15 10 0.10 a) construct the appropriate random number mappings for the random variables starting from 00. (3 marks) b) Simulate 15 customers arriving at the using the random numbers given below. (12 marks) c) What is the average time a customer waits for service? (1 mark) d) What is the average time a customer is in the system (wait plus service time) (2 marks) e) What is the percent of time the clerk is busy with customers? (2 marks) Random Numbers To Be Used in the Simulation Customer 1 2 3456 7 8 9 10 11 12 13 14 15 Interarrival time Service Time 0.72 0.08 0.87 0.15 0.04 0.52 0.46 0.96 0.1 0.46 0.96 .00 0.27 0.73 0.76 0.25 0.11 0.02 0.76 0.32 0.1 0.62 0.25 0.9 0.47 0.28 0.83 0.52 0.39 0.68 Use the following headings to complete the simulation Customer RN Time Between Arrival Begin Wait for RN Service End Time in Arrivals Time Service service Time Service System