Assignment:
Q1. Customers arrive at Rich Dunn’s Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Rich’s service times follow a negative exponential distribution, and Rich can complete an average of 5 haircuts per hour.
a) Find the average number of customers waiting for haircuts.
b) Find the average number of customers in the shop.
c) Find the average time a customer waits until it is his or her turn.
d) Find the average time a customer spends in the shop.
e) Find the percentage of time that Rich is busy.
Q2. There is only one copying machine in the student lounge of the business school. Students arrive at the rate of λ = 40 per hour (according to a Poisson distribution). Copying takes an average of 40 seconds, or μ = 90 per hour (according to a negative exponential distribution). Compute the following:
a) The percentage of time that the machine is used.
b) The average length of the queue.
c) The average number of students in the system.
d) The average time spent waiting in the queue.
e) The average time in the system.
Provide complete and step by step solution for the question and show calculations and use formulas.