God Is Not Dead Essay

1024 Words Oct 10th, 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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P (x> 3) = 1 - ∑ P (x ≤ 3) P (x> 3) = 0.03748096

f. What is the average time a customer waits for service?
Wq= 0.34175 Wq=0.1571
Problem 13
After reviewing the waiting line analysis of Problem 12, the manager of Pete´s Market wants to consider one of the following alternatives for improving service. What alternative would you recommend? Justify your recommendation. a) Improved single-server operation (µ = 30) Probability of no units in the system (Ps) | 0,3333 | Average Number of units in the line (Iq) | 1,3333 | Average Number of units in the system (L) | 2,0000 | Average Time a unit spends in the line (Wq) | 0,0667 | Average Time a unit spends in the system (W) | 0,1000 | Probability of arriving unit waiting for service (Pw) | 0,6667 |

b) Two-server operation (µ = 20 for each server) Probability of no units in the system (P0) | 0,4545 | Average Number of units in the line | 0,2700 | Average Number of units in the system | 1,0200 | Average Time a unit spends in the line | 0,0180 | Average Time a unit spends in the system | 0,0680 | Probability of arriving unit waiting for service | 0,1022 |

Problem 19
Refer again to the Lake City Regional Airport described in Problem 18. When the security level is raised to high, the service rate for processing passengers is reduced to 2 passengers per minute at each screening station. Suppose the security level is raised to high on Monday morning.

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