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sing in es) 2 2011 - May (7] (a) A car rental agency has collected the following data on the demand for five-seater vehicles over the past 50 days. Daily Demand 4 5 6 7 8 No. of Days 4 10 16 14 6 The agency has only 6 cars currently. (i). Use the following 5 random numbers to generate 5 days of demand for the rental agency. Random Nos : 15, 48, 71, 56, 90 (ii) What is the average number of cars rented per day for the 5 days? (iii) How many rentals will be lost over the 5 days?(5 marks) [CAFG - II] 2012 - May [7] Answer the following questions : (c) A refreshment centre in a railway station has two counters - (i) self- service (opted by 60% of the customers) and (ii) attended service (opted by 40% of the customers). Both counters can serve one person at a time. The arrival rate of customers is given by the following probability distribution: 95 99 2013 - Dec [8] (a) An automobile production line turns out about 100 cars a Voucher day, but deviations occur owing to many causes. The production is more accurately described by the probability distribution given below: Production per day Probability Production per day Probability 0.03 101 0.15 96 0.05 102 0.1 Yes Yes 97 0.07 103 0.07 98 0.1 104 0.05 99 0.15 105 0.03 100 0.2 Total 1 Finished cars are transported across the day, at the end of the each day, by ferry has space for only 101 cars. Required: (1) What will be the average number of cars waiting to be shipped? (ii) What will be the average area of empty space on the boat? utes The fifteen random numbers are given: 20, 63, 46, 16, 45, 41, 44, 66, 87, 26, 78, 40, 29, 92, & 21 (6 marks) 25 = Answer: minutes. Suace to write important points for revision - 2018 - Dec [6] (b) The following was the pattern for demand of cars rented out by a tourist operator observed for 100 days: No. of cars 5 7 10 15 No. of days 20 30 40 10 The random numbers are 88, 76, 10, 05, 23. Required: (i) Simulate the demand for cars over five days. (ii) How many cars should the operator have in order to have at least 75% probability of fulfilling the demand based on your simulated results? (5+3=8 marks) (Chapter 9) Simulation 15.291 2019 - June (7] (b) The following information are given: Arrival of patients Services Inter-arrival time (minutes) Probability Probability Inter-Service time (minutes) 2 0.20 4 0.25 4 0.24 6 0.34 6 0.28 8 0.26 8 0.18 10 Balance 10 Balance 402 638 The following random number are to be used for the simulation of arrival and service patterns: Arrival 740 225 906 048 421 Service 183 706 923 Required: (i) Find out the average time spent by the patient in the queue by simulation. Assume that the time starts at 6:00 a.m. and that there is only one counter and there is no time gap between finishing with one patient and starting the next patient if the next patient is already in the queue. (ii) A second counter is to be set up if the probability of waiting beyond 3 minutes exceeds 40% or if the average waiting time of a patient exceeds 5 minutes if there is a wait. Should the second counter be set up? Substantiate based on the simulation results. (8 marks)