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# BU275 BDM Mock Exam 2013

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Wilfrid Laurier University

Business

BU275

Michael Pavlin

Winter

Description

1. There is a Chinese restaurant. In a night, the diners arriving at the restaurant follows an
exponential distribution with rate 4 per twenty minutes. Probability of the interval of arriving
taking anywhere from 5 to 10 minutes
A) will be greater than the probability that the interval of arriving is between 0 to 5
minutes.
B) will be less than the probability that the interval of arriving is between 0 to 5 minutes
C) will be greater than the probability that the interval of arriving is between 10 to 15
minutes
D) will be less than the probability that the interval of arriving is between 10 to 15
minutes
E) both A) and C) are right
F) both A) and D) are right
G) both B) and C) are right
H) both B) and D) are right
2. In the restaurant mentioned in question one, diners arrive at the rate of 4 per twenty
minutes following a Poisson distribution. What is the probability of 3 arrivals in twenty-
minute interval?
e 4 3
A)
3!
e 4 4
B)
3!
e 4 3
C)
4!
4 3
D) e 4
4!
3. Still in this same restaurant in question one and two, diners arrive at the rate of 4 per
twenty minutes following a Poisson distribution. What is the probability of 5 arrivals in ten-
minute interval?
4 5
e 4
A)
5!
e 2 5
B)
5!
e 4 10
C)
10!
e 25 2
D)
2!
4. Guess what? Same restaurant that in question one, two and three, diners arrive at the rate
of 4 per twenty minutes following a Poisson distribution. Suppose the 41 diner arrive at time T1
nd
and 42 dine-4arrive at time T2, what is the probability that T2-T1> 10 minutes?
A) e-2
B) e
C) 1 – e-4
D) 1 – e-2 5. Ok, now you get it. The same restaurant that in question one, through four, diners
arrive at the rate of 4 per twenty minutes following a Poisson distribution. Probability that a
service takes between 4 and 8 minutes is equal to:
A) 0.513
B) 0.148
C) 0.247
D) 0.263
6. Remember our Chinese restaurant? It has two identical checkouts (oh, did I mention it
serves buffet?); each can serve an average of 10 diners per hour following an exponential
distribution. Diners who feel full arrive at a common checkout line following a Poisson
distribution with the same rate they are arriving, 4 per twenty minutes. The utilization of the
checkout system will be:
A) 1.2
A) 0.75
C) 0.6
D) 0.5
7 For the above checkout system in the Chinese restaurant in question 6, it is known that L =
q
0.675 and P 0 0.25. The average number in the system will be:
A) 1.875
B) 0.525
C) 0.925
C) 0.425
8. Let us calculate the cost of this beloved Chinese restaurant. The main costs of the restaurant
come from the rice! Currently they get 2 cars full of rice per hour, and car of bags of rice
cost $200.The rice delivery persons are impatient. They arrive at the backdoor of the
restaurant at the rate of 3 per hour, and they charge $100 per hour of time spent by the
person in the system. There are two people handling these rice people, each can handle 2
per hour. Arrivals are Poisson, and service is exponential. Calculations shoq L is 1.043.
The total hourly cost of service and waiting will be:
A) $400 or less
B) between $401 and $599
B) between $601 and $799
D) $800 or more
9. You are at the restaurant, and you observe the time that it takes for each customer to go
through the check out, you record the time down with unit of minutes, 1.6, 2.7, 3.2, 2.8, 9.2,
4.2, 1.2, 2.2, 0.7, 2.1. For example, 2.8 is the time the fourth customer take to check out. If
you average these you are estimating:
A) λ
B) μ
C) 1/λ
D) 1/μ
10. You want to run a simulation of this Chinese restaurant. Supposedly you want to choose a
random number uniformly distribution in the range of [10, 29]. Allowing only integer values,
picking 2-digit random numbers and associating 00-03 with 10, 04-07 with 11, etc), what
will be the simulated demand corresponding to a random number choice of 42?
A) 20
B)

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