Find the probability that the employee is idle?
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- new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Find the probability that the employee is idle. Find the proportion of the time that the employee is busy. Find the average number of people receiving and waiting to receive some information. Find the average number of people waiting in line to get some information. Find the average time a person seeking information spends in the system. Find the expected time a person spends just waiting in line to have a question answered (time in the queue).Ray is planning to open a small car-wash operation for washing just one car at a time. He must decide how much additional space to provide for waiting cars. Ray estimates that customers would arrive according to a Poisson input process with a mean rate of 1 every 4 minutes, unless the waiting area is full, in which case the arriving customers would take their cars elsewhere. The time that can be attributed to washing one car has an exponential distribution with a mean of 2 minutes. Suppose that Ray makes an average $4 per served customers. Moreover, each car space rented for waiting costs $800 per month. Ray is planning to run the car-was for 200 hours every month. 2. How much space should Ray provide for the waiting cars in order to maximize his expected net profit? (By net profit, we mean profit from car-wash operations minus the rental cost)