Show your work

Question 1:

a) A restaurant has one drive-through window. An average of 40 customers per hour arrive at the window. It takes an average of 1 minute to serve a customer. Assume that interarrival and service times are exponential. On the average, how many customers are waiting in line? [1 point]

b) A restaurant has one drive-through window. An average of 40 customers per hour arrive at the window at a restaurant. It takes an average of 1 minute to serve a customer. Assume that interarrival and service times are exponential. On the average, how long does a customer spend at the restaurant (from time of arrival to time service is completed)? [1 point]

c) Assume that interarrival times and service times of a single-chair hair-styling shop have been exhibited to be exponentially distributed. On average, two customers arrive per hour. The hairstylist serves, on average, three customers per hour. (a) What is the probability that the hairstylist remains idle? (b) What is probability that there are four or more customers in the shop? (c) On average, how much time a customer spends in the queue? (d) On average, how much time a customer spends in the system? [1 point]