QUESTION 5 A mini post office that is located inside the Millenia Mall has only been in operation since last year. The mini post office is manned by only one counter and is open from 10.00 am to 4.30 pm. Customers arrive at the post office according to the following probability distribution: Probability Time between arrival of customers (minutes) 1 2 3 4 5 6 0.15 0.20 0.10 0.25 0.10 0.20 The length of service required by customers varies according to the following probability distribution: Length of service (minutes) Probability 3 0.15 4 0.35 5 0.20 6 0.30 The post office management has decided that they should add another counter if a customer has to wait for more than 7 minutes, on average. a) Simulate the arrivals of the first 10 customers to the post office using the random number given. Time between arrival of customers 18 84 48 39 44 07 79 56 21 24 Length of Service time 49 56 09 22 68 89 62 97 77 67 b) Find the average waiting time per customers in minutes. (1 mark) c) What is the percentage of time that the counter is busy? (1 mark) d) Do you think that the mini post office should add another counter? Why? (1 mark)