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Answer :
In a single server queuing system with a Poisson arrival rate and exponential service time, and an average arrival rate of 11 customers per hour and an average service rate of 13 customers per hour, the probability of having 4 customers in the system is approximately 0.1538.
In this scenario, we can model the queuing system using the M/M/1 model, where M represents the Poisson arrival process and M represents the exponential service time. The average arrival rate is given as 11 customers per hour, and the average service rate is given as 13 customers per hour.
Using the M/M/1 queuing formula, we can calculate the probability of having a certain number of customers in the system. In this case, we want to find the probability of having 4 customers in the system.
Using the M/M/1 queuing formula or queuing software, the probability of having 4 customers in the system can be calculated as approximately 0.1538.
Therefore, the correct answer is option d: 0.1538.
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