The sandwich maker of the EE-Cole-Eye Sandwich Truck was just fired (for a reason described below) and EE-Cole-Eye needs to find a replacement. They want to make sure that the replacement is fast enough so that customers don't have to wait too long on line. Customers arrive according to a Poisson process with arrival rate 2 customers/min and sandwich makers take an exponentially distributed length of time to make a sandwich, with mean timeservice time of 29 seconds. There are no limits to the number of customers that wait for sandwiches. Consider the queue of customers and analyze it assuming it is in steady state.

1-What is the probability there are 20 customers or fewer in the system? (Round to 3 decimal places)

2-What is the probability there are exactly 5 customers in the system? (Round to 3 decimal places)

3-What is the average number of customers in the system?

4-What is the average wait time in the in the system in minutes? (Round to 3 decimal places)

5-The performance described in the previous part is unsatisfactory, and that is why the sandwich maker was fired. How fast must the new sandwich maker work (that is, what is the required ) so that the probability that there are 5 customers or fewer in the line is greater than 0.9? (Round to 3 decimal places)

6-How long does it take now to make a sandwich on average? (Answer in seconds, round to 3 decimal places)

7-What will be the average number of customers in the system with this new sandwich maker? (Round to 2 decimal places)