Deck 10: Managing Customer and Work Flows

Question 1

Leyland Motors can service an average 5 cars per hour, and the owner of Leyland Motors wants to know the probability of various customer arrival rates. Given the average arrival rate of 4 customers per hour, the owner uses the Poisson distribution to calculate the probabilities of various customer arrivals per hour.

-What is the probability of exactly 2 customers arriving within 1 hour?

A)0.0183
B)0.0733
C)0.1465
D)0.1954
E)0.1563

Answer 1

0.1465

Question 2

Leyland Motors can service an average 5 cars per hour, and the owner of Leyland Motors wants to know the probability of various customer arrival rates. Given the average arrival rate of 4 customers per hour, the owner uses the Poisson distribution to calculate the probabilities of various customer arrivals per hour.

-What is the probability of exactly 5 customers arriving within 1 hour?

A)0.0183
B)0.0733
C)0.1465
D)0.1954
E)0.1563

Answer 2

0.1563

Question 3

Leyland Motors can service an average 5 cars per hour, and the owner of Leyland Motors wants to know the probability of various customer arrival rates. Given the average arrival rate of 4 customers per hour, the owner uses the Poisson distribution to calculate the probabilities of various customer arrivals per hour.

-What is the probability that none of the customers will arrive within 1 hour?

A)0.0183
B)0.0733
C)0.1465
D)0.1954
E)0.1563

Answer 3

0.0183

Question 4

Leyland Motors can service an average 5 cars per hour, and the owner of Leyland Motors wants to know the probability of various customer arrival rates. Given the average arrival rate of 4 customers per hour, the owner uses the Poisson distribution to calculate the probabilities of various customer arrivals per hour.

-What is the probability that at least 2 of the customers will arrive within 1 hour?

A)0.0183
B)0.0733
C)0.1465
D)0.9084
E)0.0916

Question 5

Leyland Motors can service an average 5 cars per hour, and the owner of Leyland Motors wants to know the probability of various customer arrival rates. Given the average arrival rate of 4 customers per hour, the owner uses the Poisson distribution to calculate the probabilities of various customer arrivals per hour.

-What is the probability that, at most, 3 of the customers will arrive within 1 hour?

A)0.2381
B)0.4335
C)0.5665
D)0.1954
E)0.7619

Question 6

Leyland Motors can service an average 5 cars per hour, and the owner of Leyland Motors wants to know the probability of various customer arrival rates. Given the average arrival rate of 4 customers per hour, the owner uses the Poisson distribution to calculate the probabilities of various customer arrivals per hour.

-What is the probability that there will be more than 5 customers arriving within 1 hour?

A)0.1954
B)0.6288
C)0.2149
D)0.1563
E)0.7851

Question 7

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability of having exactly 4 customers arriving within 1 hour?

A)0.0107
B)0.0286
C)0.0573
D)0.0916
E)0.1221

Question 8

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability of having exactly 10 customers arriving within 1 hour?

A)0.8159
B)0.1221
C)0.1396
D)0.1241
E)0.0993

Question 9

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability of having, at most, 10 customers arriving within 1 hour?

A)0.8159
B)0.2834
C)0.1841
D)0.7166
E)0.0993

Question 10

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability of having at least 10 customers arriving within 1 hour?

A)0.8159
B)0.2834
C)0.1841
D)0.7166
E)0.0993

Question 11

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability of having more than 10 customers arriving within 1 hour?

A)0.8159
B)0.2834
C)0.1841
D)0.7166
E)0.0993

Question 12

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability of having none of the customers arriving within 1 hour?

A)0.8159
B)0.0993
C)0.1841
D)0.0003
E)0.9997

Question 13

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability of having exactly 12 customers arriving within 1 hour?

A)0.0481
B)0.9362
C)0.0638
D)0.8881
E)0.1119

Question 14

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability of having more than 12 customers arriving within 1 hour?

A)0.0481
B)0.9362
C)0.0638
D)0.8881
E)0.1119

Question 15

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability of having exactly 15 customers arriving within 1 hour?

A)0.0003
B)0.0169
C)0.0082
D)0.9918
E)0.0090

Question 16

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that exactly 10 customers will arrive in 1 hour, when the mean arrival rate is 15 customers per hour, and interarrival times are exponentially distributed?

A)0.0486
B)0.1185
C)0.0699
D)0.9301
E)0.8815

Question 17

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that more than 10 customers will arrive in 1 hour, when the mean arrival rate is 15 customers per hour, and interarrival times are exponentially distributed?

A)0.0486
B)0.1185
C)0.0699
D)0.9301
E)0.8815

Question 18

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that less than 10 customers will arrive in 1 hour, when the mean arrival rate is 15 customers per hour and interarrival times are exponentially distributed?

A)0.0486
B)0.1185
C)0.0699
D)0.9301
E)0.8815

Question 19

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that at least 10 customers will arrive in 1 hour, when the mean arrival rate is 15 customers per hour, and interarrival times are exponentially distributed?

A)0.0486
B)0.1185
C)0.0699
D)0.9301
E)0.8815

Question 20

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that, at most, 10 customers will arrive in 1 hour, when the mean arrival rate is 15 customers per hour, and interarrival times are exponentially distributed?

A)0.0486
B)0.1185
C)0.0699
D)0.9301
E)0.8815

Question 21

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that exactly 4 customers will arrive in 1 hour, when the mean arrival rate is 3 customers per hour, and interarrival times are exponentially distributed?

A)0.3528
B)0.1847
C)0.1680
D)0.8153
E)0.6472

Question 22

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that more than 4 customers will arrive in 1 hour, when the mean arrival rate is 3 customers per hour, and interarrival times are exponentially distributed?

A)0.3528
B)0.1847
C)0.1680
D)0.8153
E)0.6472

Question 23

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that less than 4 customers will arrive in 1 hour, when the mean arrival rate is 3 customers per hour, and interarrival times are exponentially distributed?

A)0.3528
B)0.1847
C)0.1680
D)0.8153
E)0.6472

Question 24

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that at least 4 customers will arrive in 1 hour, when the mean arrival rate is 3 customers per hour, and interarrival times are exponentially distributed?

A)0.3528
B)0.1847
C)0.1680
D)0.8153
E)0.6472

Question 25

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that, at most, 4 customers will arrive in 1 hour, when the mean arrival rate is 3 customers per hour, and interarrival times are exponentially distributed?

A)0.3528
B)0.1847
C)0.1680
D)0.8153
E)0.6472

Question 26

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that no customer will arrive in 1 hour, when the mean arrival rate is 3 customers per hour, and interarrival times are exponentially distributed?

A)0.1680
B)0.2240
C)0.1494
D)0.9502
E)0.0498

Question 27

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that exactly 10 customers will arrive in 1 hour, when the mean arrival rate is 3 customers per hour, and interarrival times are exponentially distributed?

A)0.0027
B)0.0008
C)0.0002
D)0.9998
E)0.0498

Question 28

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that more than 4 customers will arrive in 1 hour, when the mean arrival rate is 4 customers per hour, and interarrival times are exponentially distributed?

A)0.6288
B)0.1954
C)0.4335
D)0.5665
E)0.3712

Question 29

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that less than 2 customers will arrive in 1 hour, when the mean arrival rate is 2 customers per hour, and interarrival times are exponentially distributed?

A)0.4060
B)0.6767
C)0.3233
D)0.5940
E)0.2707

Question 30

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that exactly 30 calls arrive at a call center in an hour, when the mean arrival rate is 30 customer calls per hour, and interarrival times are exponentially distributed?

A)0.0511
B)0.0659
C)0.0702
D)0.0726
E)0.0453

Question 31

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-Calculate the mean server utilization.

A)20%
B)35%
C)50%
D)60%
E)75%

Question 32

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-Calculate the mean number of customers in the queue.

A)none
B)1.2
C)0.9
D)3.1
E)4.1

Question 33

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-Calculate the mean number of customers in the system (being served and in the queue).

A)none
B)2.6
C)1.5
D)3.4
E)4.2

Question 34

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-Calculate the mean waiting time in the queue.

A)4.5 minutes
B)2.5 minutes
C)1.5 minutes
D)3.5 minutes
E)5 minutes

Question 35

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-Calculate the mean waiting time in the system (being served and in the queue).

A)4.5 minutes
B)2.5 minutes
C)1.5 minutes
D)3.5 minutes
E)7.5 minutes

Question 36

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that there is no customer in the system at any given time?

A)20%
B)40%
C)24%
D)60%
E)36%

Question 37

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that there is 1 customer in the system at any given time?

A)20%
B)40%
C)24%
D)60%
E)36%

Question 38

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-What is the probability that there is more than 1 customer in the system at any given time?

A)20%
B)40%
C)24%
D)60%
E)36%

Question 39

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-Change the arrival rate from 12 customers per hour to 10 customers per hour. What is the probability that there is more than 1 customer in the system at any given time?

A)25%
B)50%
C)75%
D)15%
E)36%

Question 40

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-Change the arrival rate of from 12 customers per hour to 15 customers per hour. What is the probability that there is more than 1 customer in the system at any given time?

A)25.00%
B)18.75%
C)43.75%
D)56.25%
E)36.00%

Question 41

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand.

-Change the number of customers the street vendor can serve per hour from 20 to 15. What is the probability that there is more than 1 customer in the system at any given time?

A)50%
B)36%
C)64%
D)20%
E)16%

Question 42

Use the following information to determine the optimal overbooking policy for a spa center at downtown Marquette. The center's capacity is 12 guests. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per guest is $80, and the cost of lost goodwill per guest due to overbooking is approximately $40.


-Calculate the total expected profit with 12 reservations (and no overbooking).

A)$884
B)$922
C)$918
D)$960
E)Need additional information to calculate the total expected profit

Question 43

Use the following information to determine the optimal overbooking policy for a spa center at downtown Marquette. The center's capacity is 12 guests. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per guest is $80, and the cost of lost goodwill per guest due to overbooking is approximately $40.


-Calculate the total expected profit with 13 reservations (which means 1 overbooking).

A)$884
B)$922
C)$918
D)$960
E)Need additional information to calculate the total expected profit

Question 44

Use the following information to determine the optimal overbooking policy for a spa center at downtown Marquette. The center's capacity is 12 guests. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per guest is $80, and the cost of lost goodwill per guest due to overbooking is approximately $40.


-Calculate the total expected profit with 14 reservations (which means 2 overbookings).

A)$884
B)$922
C)$918
D)$960
E)Need additional information to calculate the total expected profit

Question 45

Use the following information to determine the optimal overbooking policy for a spa center at downtown Marquette. The center's capacity is 12 guests. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per guest is $80, and the cost of lost goodwill per guest due to overbooking is approximately $40.


-Based on the total expected profits obtained in Questions 41 through 43, which policy should be selected?

A)More than 14 reservations
B)12 reservations (that implies no overbooking)
C)14 reservations (that implies 2 overbookings)
D)13 reservations (that implies 1 overbooking)
E)Need additional information to calculate the total expected profit

Question 46

Use the following information to determine the optimal overbooking policy for a motel at a rural town in South Carolina. The motel's capacity is 30 rooms. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per room is $110, and the cost of lost goodwill per guest due to overbooking is approximately $60.


-Calculate the total expected profit with 30 reservations (and no overbooking).

A)$3,300.00
B)$2,886.00
C)$2,897.50
D)$2,883.50
E)$3,146.00

Question 47

Use the following information to determine the optimal overbooking policy for a motel at a rural town in South Carolina. The motel's capacity is 30 rooms. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per room is $110, and the cost of lost goodwill per guest due to overbooking is approximately $60.


-Calculate the total expected profit with 31 reservations (which means 1 overbooking).

A)$3,300.00
B)$2,886.00
C)$2,897.50
D)$3,213.50
E)$2,827.00

Question 48

Use the following information to determine the optimal overbooking policy for a motel at a rural town in South Carolina. The motel's capacity is 30 rooms. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per room is $110, and the cost of lost goodwill per guest due to overbooking is approximately $60.


-Calculate the total expected profit with 32 reservations (which means 2 overbookings).

A)$3,300.00
B)$2,886.00
C)$2,897.50
D)$3,221.50
E)$2,827.00

Question 49

Use the following information to determine the optimal overbooking policy for a motel at a rural town in South Carolina. The motel's capacity is 30 rooms. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per room is $110, and the cost of lost goodwill per guest due to overbooking is approximately $60.


-Calculate the total expected profit with 33 reservations (which means 3 overbookings).

A)$3,300.00
B)$3,204.00
C)$2,897.50
D)$2,883.50
E)$2,827.00

Question 50

Use the following information to determine the optimal overbooking policy for a motel at a rural town in South Carolina. The motel's capacity is 30 rooms. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per room is $110, and the cost of lost goodwill per guest due to overbooking is approximately $60.


-Based on the total expected profits obtained in Questions 46 through 49, which policy should be selected?

A)More than 33 reservations
B)30 reservations (that implies no overbooking)
C)33 reservations (that implies 3 overbookings)
D)31 reservations (that implies 1 overbooking)
E)32 reservations (that implies 2 overbookings)