Question

Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 5 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions:
What is the probability that one customer is receiving a haircut and one customer is waiting?

What is the probability that one customer is receiving a haircut and two customers are waiting?

What is the probability that more than two customers are waiting?

Answer 1

Answer:

Step-by-step explanation:

Arrival rate = ∧ = 2.2 customers per hour

Service rate = u = 5 customers per hour

1. Probability that one customer is receiving a haircut and one customer is waiting

P(2 customers)=(∧/u)^2 * (1-∧/u)=(2.2/5)^2 * (1-2.2/5)=0.1936*0.56= 0.108416

2. Probability that one customer is receiving a haircut and two customers are waiting

P(3 customers)= (∧/u)^3 * (1-∧/u)=(2.2/5)^3 * (1-2.2/5)= 0.085184

* 0.56= 0.04770304

3. Probability that more than two customers are waiting

P(more than 3 customers)=1- P(less than 3 customers) =

1- [P(0)+P(1)+P(2)+P(3)]=

= 1- [(1-2.2/5) +2.2/5*(1- 2.2/5) + 0.108416+0.04770304]=1-0.9625=0.0375

3. Probability that more than two customers are waiting =