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God Is Not Dead

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Submitted By mairaroca228
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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 probabilities of the described scenarios are as follows:
P0=20e-20! P0=0.135335283
P1=21e-21! P1=0.270670566
P2=22e-22! P2=0.270670566
P3=23e-23! P3=0.180447044

c) Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur?
This probability can be expressed as the probability of more than 3 customers arriving during the five-minute period, which can be computed as following:
P(x > 3) = 1 – P(x ≤ 3) P (x > 3) = 1 – 0.85712346
P(x > 3) = 0.14287654

Thus, there is a 14, 29% probability of expected delays in five-minute period.

Problem 3
Use the single-server drive-up bank teller operation referred to in Problems 1 and 2 to determine the following characteristics for the system: Using arrival rate and service rate PER MINUTE a) The probability that no customers are in the system
P0=1- 0.40.6 P0=0.3333 b) The average number of customers waiting
Lq=0.420.6(0.6-0.4) Lq=1.3333 c) The average number of customers waiting
L = 1.3333 + 0.40.6 L = 2 d) The average time a customer’s spends waiting
Wq= 1.33330.4 Wq=3.3333...

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