A new restaurant just opened-up in a town near you

A new restaurant just opened-up in a town near you. The manager of this establishment has asked you to evaluate their drive-thru system queue. More specifically, the restaurant owner wishes to better understand the relationship between service rates and the resulting average amount of time a customer spends in the system. The manager has a choice in the number of servers working ranging from a minimum of 8 servers to a maximum of 15 servers (only consider integers values of servers). The restaurant's average service rate is a function of the number of servers working such that (number_of_servers*5 = average_customers_serviced_per_hour). Assuming that the restaurant meets M/M/1 model assumptions and has an average arrival rate of 37 customers/hour, what is the minimum number of servers required to meet the threshold maximum time of 5 minutes for average time a customer spends in the system?
A. 8 servers
B. 9 servers
C. 10 servers
D. 11 servers
E. 12 servers


Using the same model assumptions as the first part of the question, and assuming your answer being 13 servers and service rate as its corresponding average_service_rate (5*servers=average_service_rate_per_hour), what is the probability that exactly 5 customers are in the system? (round to nearest hundredth of a percent)
A. 5.77%
B. 19.24%
C. 10.54%
D. 2.57%