please answer all Marty's Barber Shop has one barber. Customers have an arrival rate of 1.6 customers per hour, and haircuts are givenwith a service rate of 3 per hour. Use the Poisson arrivals and exponential service times model to answer the followingquestions:a. What is the probability that no units are in the system? Round your answer to four decimal places.Po =b. What is the probability that one customer is receiving a haircut and no one is waiting? Round your answer to fourdecimal places.P₁ =c. What is the probability that one customer is receiving a haircut and one customer is waiting? Round your answer tofour decimal places.P2 =d. What is the probability that one customer is receiving a haircut and two customers are waiting? Round your answerto four decimal places.P3 =e. What is the probability that more than two customers are waiting? Round your answer to four decimal places.P(More than 2 waiting)= The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrivalrate of 8 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distributionwith a service rate of 11 requests per hour.a. What is the probability that no requests for assistance are in the system? If required, round your answer to four decimal places.Po =b. What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places.Lq =c. What is the average waiting time in minutes before service begins? If required, round your answer to nearest whole number.Wq =d. What is the average time at the reference desk in minutes (waiting time plus service time)? If required, round your answer to nearestwhole number.W =minPw=mine. What is the probability that a new arrival has to wait for service? If required, round your answer to four decimal places.

Hi thank you for posting this question, since you have posted multiple question we have solve first…

Marty's Barber Shop has one barber. Customers have an arrival rate of 1.6 customers per hour, and haircuts are given with a service rate of 3 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: a. What is the probability that no units are in the system? Round your answer to four decimal places. Po = b. What is the probability that one customer is receiving a haircut and no one is waiting? Round your answer to four decimal places. P₁ = c. What is the probability that one customer is receiving a haircut and one customer is waiting? Round your answer to four decimal places. P2 = d. What is the probability that one customer is receiving a haircut and two customers are waiting? Round your answer to four decimal places. P3 = e. What is the probability that more than two customers are waiting? Round your answer to four decimal places. P(More than 2 waiting) =

Marty's Barber Shop has one barber. Customers have an arrival rate of 1.6 customers per hour, and haircuts are given with a service rate of 3 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: a. What is the probability that no units are in the system? Round your answer to four decimal places. Po = b. What is the probability that one customer is receiving a haircut and no one is waiting? Round your answer to four decimal places. P₁ = c. What is the probability that one customer is receiving a haircut and one customer is waiting? Round your answer to four decimal places. P2 = d. What is the probability that one customer is receiving a haircut and two customers are waiting? Round your answer to four decimal places. P3 = e. What is the probability that more than two customers are waiting? Round your answer to four decimal places. P(More than 2 waiting) =

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

please answer all

Marty's Barber Shop has one barber. Customers have an arrival rate of 1.6 customers per hour, and haircuts are given
with a service rate of 3 per hour. Use the Poisson arrivals and exponential service times model to answer the following
questions:
a. What is the probability that no units are in the system? Round your answer to four decimal places.
Po =
b. What is the probability that one customer is receiving a haircut and no one is waiting? Round your answer to four
decimal places.
P₁ =
c. What is the probability that one customer is receiving a haircut and one customer is waiting? Round your answer to
four decimal places.
P2 =
d. What is the probability that one customer is receiving a haircut and two customers are waiting? Round your answer
to four decimal places.
P3 =
e. What is the probability that more than two customers are waiting? Round your answer to four decimal places.
P(More than 2 waiting)
=

The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival
rate of 8 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution
with a service rate of 11 requests per hour.
a. What is the probability that no requests for assistance are in the system? If required, round your answer to four decimal places.
Po =
b. What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places.
Lq =
c. What is the average waiting time in minutes before service begins? If required, round your answer to nearest whole number.
Wq =
d. What is the average time at the reference desk in minutes (waiting time plus service time)? If required, round your answer to nearest
whole number.
W =
min
Pw=
min
e. What is the probability that a new arrival has to wait for service? If required, round your answer to four decimal places.

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