Question 1

From a portion of a probability distribution,you read that P(demand = 0)is 0.05 and P(demand = 1)is 0.10.The cumulative probability for demand = 1 would be which of the following?
A)0.05
B)0.075
C)0.10
D)0.15
E)0.005

Accepted Answer

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Question 2

The ________ method is a simulation technique that uses random elements when chance exists in their behavior.

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Question 3

A distribution of service times at a waiting line indicates that service takes 12 minutes 30 percent of the time and 14 minutes 70 percent of the time.In preparing this distribution for Monte Carlo analysis,the service time 13 minutes would be represented by what random number range?
A)00 through 29
B)01 through 30
C)30 through 99
D)31 through 00
E)None of these;13 minutes is not a possible outcome.

Accepted Answer

The service times given are 12 minutes (30% of the time) and 14 minutes (70% of the time). There is no mention of a 13-minute service time, making it not a possible outcome based on the provided distribution. Monte Carlo analysis uses the given probabilities, and since 13 minutes is not included, it cannot be represented in the random number range.

Question 4

Explain how Monte Carlo simulation uses random numbers.

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Question 5

From a portion of a probability distribution,you read that P(demand = 1)is 0.05,P(demand = 2)is 0.15,and P(demand = 3)is .20.The cumulative probability for demand = 3 would be which of the following?
A)0.133
B)0.200
C)0.400
D)0.600
E)Cannot be determined from the information given.

Accepted Answer

The answer of From a portion of a probability distribution,you...

Question 6

A distribution of service times at a waiting line indicates that service takes 6 minutes 30 percent of the time,7 minutes 40 percent of the time,8 minutes 20 percent of the time,and 9 minutes 10 percent of the time.In preparing this distribution for Monte Carlo analysis,the service time of 8 minutes would be represented by what random number range?
A)20 through 40
B)21 through 40
C)70 through 90
D)71 through 90
E)01 through 20

Accepted Answer

To represent the service time of 8 minutes in Monte Carlo analysis, we can randomly select a number within the range of 70 through 89. This is because the service time of 8 minutes occurs 20% of the time and we can represent this percentage by choosing a range of random numbers that corresponds to 20% of the total range of possible numbers (i.e. 100). 
70 through 89 covers a range of 20 numbers out of 100, which represents the 20% probability of service time being 8 minutes.

Question 7

A distribution of service times at a waiting line shows that service takes 6 minutes 30 percent of the time,7 minutes 40 percent of the time,8 minutes 20 percent of the time,and 9 minutes 10 percent of the time.This distribution has been prepared for Monte Carlo analysis.The first two random numbers drawn are 53 and 74.The simulated service times are ________ minutes,then ________ minutes.
A)6;7
B)7;7
C)7;8
D)8;9
E)Cannot determine because no service time probability is that large.

Accepted Answer

To use the given distribution for Monte Carlo simulation, we need to convert the percentages into cumulative probabilities: 
- 6 minutes has a cumulative probability of 0.30
- 7 minutes has a cumulative probability of 0.70 (0.30+0.40)
- 8 minutes has a cumulative probability of 0.90 (0.30+0.40+0.20)
- 9 minutes has a cumulative probability of 1.00 (0.30+0.40+0.20+0.10)

Now, we can use the first random number (53) to generate a service time by finding the interval that includes 0.53 on the cumulative probability scale:
- 0.53 is between 0.30 and 0.70, so the service time is 7 minutes.

For the second random number (74), we repeat the process by finding the interval that includes 0.74:
- 0.74 is between 0.70 and 0.90, so the service time is 8 minutes.

Therefore, the simulated service times are 7 minutes and then 8 minutes. The best choice is (C).

Question 8

Setting up a probability distribution,building a cumulative probability distribution,and generating random numbers are:
A)necessary when the underlying probability distribution is normal.
B)three of the five steps in Monte Carlo simulation.
C)elements of physical simulation but not mathematical simulation.
D)the elements of the threefold idea behind simulation.
E)advantages of simulation.

Accepted Answer

These are indeed three of the five steps involved in conducting a Monte Carlo simulation, which is a technique used to understand the impact of risk and uncertainty in prediction and forecasting models.

Question 9

The numbers used to represent each possible value or outcome in a computer simulation are referred to as ________.

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The answer of The numbers used to represent each possible...

Question 10

From a portion of a probability distribution,you read that P(demand = 0)is 0.05,P(demand = 1)is 0.10,and P(demand = 2)is 0.20.What are the two-digit random number intervals for this distribution beginning with 01?
A)01 through 05,01 through 10,and 01 through 20
B)00 through 04,05 through 14,and 15 through 34
C)01 through 05,06 through 15,and 16 through 35
D)00 through 04,00 through 09,and 00 through 19
E)01 through 06,07 through 16,and 17 through 36

Accepted Answer

To determine the two-digit random number intervals, you need to add up the probabilities starting from the lowest possible value. So, for demand = 0, the interval would be 01 through 05 (0.05 probability). For demand = 1, the interval would be 06 through 15 (0.10 probability added to the previous interval). Finally, for demand = 2, the interval would be 16 through 35 (0.20 probability added to the previous interval). This gives us the intervals 01 through 05, 06 through 15, and 16 through 35, which matches choice C.

Question 11

From a portion of a probability distribution,you read that P(demand = 0)is 0.25,and P(demand = 1)is 0.30.What are the random number intervals for this distribution beginning with 01?
A)01 through 25,and 26 through 30
B)01 through 25,and 01 through 30
C)01 through 25,and 26 through 55
D)00 through 25,and 26 through 55
E)00 through 25,and 26 through 30

Accepted Answer

Since the given probabilities are for demand = 0 and demand = 1, the intervals should cover all possible values of demand. The intervals for demand = 0 can be from 01 to 25 (as P(demand = 0) is 0.25). The intervals for demand = 1 can be from 26 to 55 (as P(demand = 1) is 0.30). Therefore, the random number intervals for this distribution beginning with 01 are 01 through 25 and 26 through 55. Choice C is the only option that includes both of these intervals.

Question 12

A(n)________ is a series of digits that have been selected by a totally random process.

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Question 13

Identify,in order,the five steps required to implement the Monte Carlo simulation technique.

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Question 14

The number of tires sold at a car garage varies randomly between 0 and 4 each hour,with equally probability for each possible outcome.What set of random numbers (on the 01-100 scale)would tire sales of 2 be assigned?
A)01 through 20
B)21 through 40
C)41 through 60
D)51 through 75
E)26 through 50

Accepted Answer

Since there are 5 possible outcomes (0, 1, 2, 3, 4) and each has an equal probability, each outcome is assigned 20% of the 01-100 scale. For tire sales of 2, which is the third outcome, it would be assigned the third segment of 20%, which is 41 through 60.

Question 15

A(n)________ is the accumulation of individual probabilities of a distribution.

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Question 16

A distribution of lead times in an inventory problem indicates that lead time was 1 day 20 percent of the time,2 days 30 percent of the time,3 days 30 percent of the time,and 4 days 20 percent of the time.This distribution has been prepared for Monte Carlo analysis.The first four random numbers drawn are 06,63,57,and 02.What is the average lead time of this simulation?
A)1.75 days
B)2 days
C)3 days
D)3.5 days
E)8 days

Accepted Answer

We use the first two digits of each of the four random numbers drawn to simulate lead time. 
- For the first random number (06), we take the first two digits (06) and find that lead time is 1 day. 
- For the second random number (63), we take the first two digits (63) and find that lead time is 3 days. 
- For the third random number (57), we take the first two digits (57) and find that lead time is 2 days. 
- For the fourth random number (02), we take the first two digits (02) and find that lead time is 1 day.

To find the average lead time of the simulation, we add up the lead times and divide by the number of lead times simulated:

(1 + 3 + 2 + 1) / 4 = 7 / 4 = 1.75

Therefore, the average lead time of this simulation is 1.75 days. The correct answer is (A).

Question 17

What is the Monte Carlo method?

Accepted Answer

The answer of What is the Monte Carlo method?...

Question 18

Which of the following is NOT a step in running a Monte Carlo simulation?
A)setting up a probability distribution for important variables
B)building a cumulative probability distribution for each variable
C)establishing an interval of random numbers for each variable
D)generating random numbers
E)All of the above are steps in running a Monte Carlo simulation.

Accepted Answer

The answer of Which of the following is NOT a...

Question 19

A distribution of service times at a waiting line indicates that service takes 12 minutes 30 percent of the time and 14 minutes 70 percent of the time.This distribution has been prepared for Monte Carlo analysis.The first four random numbers drawn are 07,60,77,and 49.What is the average service time of this simulation?
A)12 minutes
B)13 minutes
C)13.5 minutes
D)14 minutes
E)54 minutes

Accepted Answer

According to the distribution, service takes 12 minutes 30% of the time and 14 minutes 70% of the time. So, if the first random number (07) falls within the first 30%, the service time will be 12 minutes. If it falls within the remaining 70%, the service time will be 14 minutes. The first random number (07) falls within the first 30%, so the service time is 12 minutes. The next three random numbers do not affect the service time, so they can be ignored. Therefore, the average service time of this simulation is (12 minutes + 0 + 0 + 0)/4 = 3 minutes = 12.75 minutes. Rounded to the nearest half minute, the answer is 13.5 minutes.

Question 20

What is the cumulative probability of selling 4 tires? 
A)1
B).5
C)10
D).2
E).25

Accepted Answer

The answer of What is the cumulative probability of selling...

Quiz 27: Modeling with Simulation

From a portion of a probability distribution,you read that P(demand = 0) is 0.05 and P(demand = 1) is 0.10.The cumulative probability for demand = 1 would be which of the following?

The ________ method is a simulation technique that uses random elements when chance exists in their behavior.

A distribution of service times at a waiting line indicates that service takes 12 minutes 30 percent of the time and 14 minutes 70 percent of the time.In preparing this distribution for Monte Carlo analysis,the service time 13 minutes would be represented by what random number range?

Explain how Monte Carlo simulation uses random numbers.

From a portion of a probability distribution,you read that P(demand = 1) is 0.05,P(demand = 2) is 0.15,and P(demand = 3) is .20.The cumulative probability for demand = 3 would be which of the following?

Setting up a probability distribution,building a cumulative probability distribution,and generating random numbers are:

The numbers used to represent each possible value or outcome in a computer simulation are referred to as ________.

From a portion of a probability distribution,you read that P(demand = 0) is 0.05,P(demand = 1) is 0.10,and P(demand = 2) is 0.20.What are the two-digit random number intervals for this distribution beginning with 01?

From a portion of a probability distribution,you read that P(demand = 0) is 0.25,and P(demand = 1) is 0.30.What are the random number intervals for this distribution beginning with 01?

A(n)________ is a series of digits that have been selected by a totally random process.

Identify,in order,the five steps required to implement the Monte Carlo simulation technique.

The number of tires sold at a car garage varies randomly between 0 and 4 each hour,with equally probability for each possible outcome.What set of random numbers (on the 01-100 scale) would tire sales of 2 be assigned?

A(n)________ is the accumulation of individual probabilities of a distribution.

What is the Monte Carlo method?

Which of the following is NOT a step in running a Monte Carlo simulation?

What is the cumulative probability of selling 4 tires?