# Waiting line model - Queuing Theory

Question 1 Produce trucks arrive at the weigh station at the California border at a rate of 3 per hour according to a Poisson distribution. Livestock trucks arrive at that same weigh station at a rate of 2 per hour according to a Poisson distribution. What is the probability that the number of livestock trucks arriving at the weigh station in two hours is less than 3?

Question 2 The fraction nonconforming of assembled parts is under investigation. A completely randomized sample of 150 parts has been tested revealing that 8 are nonconforming. Can it be concluded that the fraction of nonconforming parts is greater than 0.05? Use Type I error of .01. Show ALL work, hypothesis, computations, rationale, and clearly state your conclusion.

Question 3 An average of 10 cars per hour arrive at a single server drive in bank teller. The inter arrival time is distributed exponentially. The average service time for each customer is exponentially distributed with a mean of 4 minutes. What fraction of the time is the server idle?

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#### Solution Preview

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Question 1 Produce trucks arrive at the weigh station at the California border at a rate of 3 per hour according to a Poisson distribution. Livestock trucks arrive at that same weigh station at a rate of 2 per hour according to a Poisson distribution. What is the probability that the number of livestock trucks arriving at the weigh ...

#### Solution Summary

This post solves three problems on waiting line models specifically answering probability that the number of livestock trucks arriving at the weigh station in two hours is less than 3, idle time for server and non-conforming parts in a sample.