Q51282 A factory produces 150 scooters. But the production rate varies with the distribution depicted in table 1.

Production Rate	147	148	149	150	151	152	153
Probability	0.05	0.10	0.15	0.20	0.30	0.15	0.05

Table 1: Production Rate and Probability

At present the track will hold 150 scooters. Using the following random numbers determine the average number of scooters waiting for shipment in the factory and average number of empty space in the truck. Random Numbers 82, 54, 50, 96, 85, 34, 30, 02, 64, 47.

Solution

Table 2 depicts the production rate and probability.

Production rate	Probability	Cumulative Probability	Random No. Assigned
147	0.05	0.05	00 – 04
148	0.10	0.15	05 – 14
149	0.15	0.30	15 – 29
150	0.20	0.50	30 – 49
151	0.30	0.80	50 – 79
152	0.15	0.95	80 – 94
153	0.05	1.00	95 – 99

Table 2 Production Rate and Probability

Table 3 depicts the simulation worksheet.

Trial No.	Random No.	Simulated Production Rate	Scooter Waiting in the factory	Number of example spaces in the truck
1	82	152	2	–
2	54	150	2	–
3	50	150	2	–
4	96	153	5	–
5	85	152	7	–
6	34	150	7	–
7	30	150	7	–
8	02	147	4	3
9	64	151	5	–
10	47	150	7	–
	Total			3

Table 3: Simulation Worksheet

Therefore, average number of scooters waiting = 7/10 =0.7/day
Average number of empty space = 3/10 = 0.3/day

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