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What will be the average number of scooters waiting in the factory?

The automobile company manufactures around 150 scooters. The daily production varies from 146 to 154 depending upon the availability of raw materials and other working conditions: -

Production per day Probability
146 0.04
147 0.09
148 0.12
149 0.14
150 0.11
151 0.10
152 0.20
153 0.12
154 0.08

The finished scooters are transported in a specially arranged lorry accommodating 150 scooters. Using the random numbers 80, 81, 76, 75, 64, 43, 18, 26, 10, 12, 65, 68, 69, 61, 57, simulate the process to find out: - i. What will be the average number of scooters waiting in the factory? - ii. What will be the average number of empty space on the lorry? -

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Production per day Probability Cumulative Probability Random Numbers Assigned
146 0.04 0.04 00-03
147 0.09 0.13 04-12
148 0.12 0.25 13-24
149 0.14 0.39 25-38
150 0.11 0.50 39-49
151 0.10 0.60 50-59
152 0.20 0.80 60-79
153 0.12 0.92 80-91
154 0.08 1.00 92-99

Using the given random numbers, the process is simulated:

Lorry capacity = 150

Day Random Number Production Can be transported in Lorry Scooters waiting at factory Cumulative no. of Scooters waiting at factory Scooters actually transported by Lorry
1 80 153 150 3 3 150
2 81 153 150 3 6 150
3 76 152 150 2 8 150
4 75 152 150 2 10 150
5 54 151 150 1 11 150
6 43 150` 150 0 11 150
7 18 148 148 - 9 150
8 26 149 149 - 8 150
9 10 147 147 - 5 150
10 12 147 147 - 2 150
11 65 152 150 2 4 150
12 68 152 150 2 6 150
13 69 152 150 2 8 150
14 61 152 150 2 10 150
15 57 151 150 1 11 150


    1.Average number of scooters waiting at the factory:

    Total number of scooters waiting at the factory over the 15 day period: 3+3+2+2+1+2+2+2+2+1 = 20

    Therefore average number waiting = 20 / 15 = 1.33 / day

    Or 20 / 15 day period


    2.Average number of empty spaces in the lorry:

    As evident from the table above, in any 15-day period, the lorry always goes full.

    Hence there is no empty space in the lorry.

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