5. Suppose your internet connection has slowed down and you are thinking about calling the helpline...

  

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5. Suppose your internet connection has slowed down and you are thinking about calling the helpline of your local Internet Service Provider. You know that the helpline is staffed by only one representative and the average duration of a call from customers to the helpline is 30 minutes (this includes time spent on hold and in talking to the representative). What is the probability that your call will take more than 1 hour (including time spent on hold and in talking to a representative)? Assume that inter-arrival times and service times are both exponentially distributed. Please enter your answer as a value between 0 and 1. If your answer is not an integer, provide at least three decimal places, e.g., 7.500. 6. Consider a single server queueing system with a mean job arrival rate of 6 jobs/hour and a mean service time of 6 minutes. What is the probability that there are one or more jobs waiting in the queue to receive service? Please enter your answer as a value between 0 and 1. If your answer is not an integer, provide at least three decimal places, e.g., 7.500. Hint: You need to carefully think about how many jobs should be in the system so that one or more jobs are waiting in the queue! 5. Suppose your internet connection has slowed down and you are thinking about calling the helpline of your local Internet Service Provider. You know that the helpline is staffed by only one representative and the average duration of a call from customers to the helpline is 30 minutes (this includes time spent on hold and in talking to the representative). What is the probability that your call will take more than 1 hour (including time spent on hold and in talking to a representative)? Assume that inter-arrival times and service times are both exponentially distributed. Please enter your answer as a value between 0 and 1. If your answer is not an integer, provide at least three decimal places, e.g., 7.500. 6. Consider a single server queueing system with a mean job arrival rate of 6 jobs/hour and a mean service time of 6 minutes. What is the probability that there are one or more jobs waiting in the queue to receive service? Please enter your answer as a value between 0 and 1. If your answer is not an integer, provide at least three decimal places, e.g., 7.500. Hint: You need to carefully think about how many jobs should be in the system so that one or more jobs are waiting in the queue!