A fast food restaurant has customers arrive at the checkout counter at a rate of 30 customers per hour. The average check out time at the till is 90 seconds.
a) What is the utilization? What is probability that there are zero customers at the counter (either in line or being served)? What is the probability that there are two or more customers at the checkout counter?
b) What is the probability that there are 1 or 2 customers at the counter? What is the average number of customers waiting in line?
c) If the store wanted the average time in the system to be 5 minutes, what would the service rate have to be? What is the probability that checkout time will take between 1 and 2 minutes? What is the probability that checkout time will take more than 2 minutes?