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- 2013 - Dec [8] (a) An automobile production line turns out about 100 cars a 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 95 0.03 101 0.15 96 0.05 102 0.1 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: () 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? The fifteen random numbers are given: 20, 63, 46, 16, 45, 41, 44, 66, 87, 26, 78, 40, 29, 92, & 21 (6 marks) S igned 09 99 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) Scrap 2019 - June [7] (b) The following information are given: Arrival of patients Services Inter-arrival time Probability Inter-Service (minutes) time (minutes) Probability 4 0.25 2. 0.20 0.24 6 4 0.34 6 0.28 8 0.26 8 0.18 10 Balance 10 Balance The following random number are to be used for the simulation of arrival and service patterns: Arrival 740 225 906 048 421 Service 402 183 706 923 638 Required: ( 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. () 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) 2012 - Nov [3] (b) An international tourist company deals with numerous personal callers each day and prides itself on its level of service. The time to deal with each caller depends on the client's requirements which range froin, say, a request for a brochure to booking a round-the-world cruise. If a client has to wait for more than 10 minutes for attention, it is company's policy for the manager to see him personally and to give him a holiday voucher worth 15. The company's observations have shown that the time taken to deal with clients and the arrival pattern of their calls follow the following distribution pattern: Scanner CMA 15.284 20 30 14 6 10 4 2 0.10 0.06 Mnutes 0.30 0.25 Time to deal 0.15 Probability 0.06 0.10 with dients 15 25 1 8 Mnutes Time between 0.3 0.1 call arrivals Probability 0.2 0.4 Required: (1) Describe how you would simulate the operation of the travel agency based on the use of random number tables; (ii) Simulate the arrival and serving of 12 clients and show the number of clients who receive a voucher (use line 1 of the random numbers below to derive the arrival pattern and line 2 for serving times); and (iii) Calculate the weekly cost of vouchers, assuming the proportion of clients receiving vouchers derived from (ii) applies throughout a week of 75 operating hours. Random Numbers Line 1 3 47 43 73 86 36 96 47 36 61 46 98 Line 2 63 71 62 33 26 16 80 45 60 11 14 10. (7 marks) [CAFG PRACTICAL QUI me. om the 36 2010 - May [5] (a) ABC Cooperative Bank receives and disburses different amount of cash in each month. The bank has an opening cash Balance of 215 crores in the first month. Pattern of receipts and disbursements from past data is as follows: Monthly Cash receipts Monthly Cash disbursements in Crores Probability in Crores Probability 0.15 30 33 0.20 42 0.40 60 0.20 0.25 39 0.40 99 0.15 57 0.25 Simulate the cash position over a period of 12 months. Required: () Calculate probability that the ABC Cooperative Bank will fall short in payments. ) Calculate average monthly shortfall. (ii) If ABC Bank can get an overdraft facility of * 45 crores from other Nationalized banks. What is the probability that they will fall short in monthly payments? Use the following sequence (rowwise) of paired random numbers. 1778 4316 7435 3123 7244 4692 5158 6808 9358 5478 9654 0977 (7 marks) (CAFG - II) 2011 - Nov [7] Answer the following questions: (a) What are the steps involved in the simulation process? (4 marks - to me. om he e 2010 - May [5] (a) ABC Cooperative Bank receives and disburses different amount of cash in each month. The bank has an opening cash Balance of 15 crores in the first month. Pattern of receipts and disbursements from past data is as follows: Monthly Cash receipts Monthly Cash disbursements in Crores in Crores Probability ty Probability 0.15 30 33 0.20 42 0.40 60 0.20 36 0.25 39 0.40 99 0.15 57 0.25 Simulate the cash position over a period of 12 months. Required: (0) Calculate probability that the ABC Cooperative Bank will fall short in payments. (ii) Calculate average monthly shortfall. (iii) If ABC Bank can get an overdraft facility of 45 crores from oth Nationalized banks. What is the probability that they will fall short in monthly payments? Use the following sequence (rowwise) of paired random numbers. 1778 4316 7435 3123 7244 4692 5158 6808 9358 5478 9654 0977 (7 marks) [CAFG