Patients arrive at Max hospital for X-ray according to a Poissonprocess. There is an X-ray machine and arriving patients form asingle line that feeds the X-ray machine in afirst-come-first-served order. Past data show that the average waitfor a patient is 30 minutes. The service time in the process takes,on an average, 10 minutes, exponentially distributed. a)Averagenumber of patients in the system b)Average number of patients inthe queue c)Average time a patient spends in the system d)What isthe arrival rate? e)Probability that the server is idlef)Probability that there is at least one patient in the systemg)Probability that there are less than or equal to 3 patients inthe system h)Probability that there are 3 patients in the systemi)Probability that there are more than or equal to 2 but less thanor equal to 3 patients in the system
