Question: 3. Tracks at a single platform weigh-bridge arrive according to Poisson probability distribution. The time required to weigh the trucks follows an exponential probability distribution.

3. Tracks at a single platform weigh-bridge

3. Tracks at a single platform weigh-bridge arrive according to Poisson probability distribution. The time required to weigh the trucks follows an exponential probability distribution. The mean arrival rate is 12 trucks per day and the mean service rate is 18 trucks per day. Determine a) The number of trucks in the system. [2 Marks] b) The average time in hours, a truck waits for weighing service to begin given that the weigh bridge operates 24 hours a day. c) The average number of trucks waiting for service. [3 Marks] d) The probability that out of 10 tracks arriving, 3 will be in the system

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