Essay on God Is Not Dead

1031 Words Oct 15th, 2015 5 Pages
CHAPTER 15
Problem 1
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute. a) What is the mean or expected number of customers that will arrive in a five-minute period?
The expected number is of 0.4*5 = 2 customer is a five-minute period. b) Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period.
The
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Customers provide an arrival rate of 2.5 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution. a. What is the average number of cars in the system?
Lq= 2.525(5-2.5) Lq=0.5
L=5+ 0.52.5 L = 1 b. What is the average time that a car waits for the oil and lubrication service to begin?
Wq= 0.52.5 W = 0.2 c. What is the average time a car spends in the system?
W = 0.2 + 15 W = 0.4 d. What is the probability that an arrival has to wait for service?
Pw= 2.55 Pw=0.5

Problem 9
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 time’s model to answer the following questions: a. What is the probability that no units are in the system?
P0=1- 2.25 P0=0.56 b. What is the probability that one customer is receiving a haircut and no one is waiting?
P1=(2.25)1*0.56 P1=0.2464

c. What is the probability that one customer is receiving a haircut and one customer is waiting?
P2=(2.25)2*0.56 P3=0.108416

d. What is the probability that one customer is receiving a haircut and two

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