Question 1

A student wants to simulate rainy and sunny days in her town for a three-week period.What is the minimum number of digits the student must obtain from a random number table for each observation,if it rained on two-fifths of the days over the past several years at this time of the year? Assume that days can be classified historically as either sunny or rainy.
A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

The answer of A student wants to simulate rainy and...

Question 2

On cold mornings,the probability that David's car won't start is .22.When it doesn't start,he takes the bus and is late for work.When it does start,he drives to work on the freeway.Sixty-five percent of the time the freeway is clear,and he gets to work on time.The rest of the time he is late.Simulate 10 consecutive days' worth of trips to work using the random numbers given.Use the lower numbers in each string to represent "car won't start" and "freeway clear".

Accepted Answer

The answer of On cold mornings,the probability that David's car...

Question 3

Customers arrive at a retail store at an average rate of five per hour.The time between arrivals can be described by an Exponential distribution.Assuming a customer has just arrived (time = 12: 00 pm),find the arrival time for next two customers.Using the following random digits (left to right):
27,05
A) 12:16 PM. and 12:36 PM
B) 12:27 PM and 12:32 PM
C) 12:05 PM and 12:27 PM
D) 12:32 PM and 12:59 PM
E) none of the choices are correct.

Accepted Answer

The exponential distribution with a rate of 5 per hour has a mean of 12 minutes per arrival. Using the random digits 27 and 05, convert them to probabilities (0.27 and 0.05) and use the inverse exponential function to find the time between arrivals. The first customer arrives at 12:16 PM (12 + 0.27*12) and the second at 12:36 PM (16 + 0.05*12).

Question 4

Which of the following is not a reason for simulation's popularity?
A) It is simple to use and/or understand.
B) Extensive software packages are available.
C) Many situations are too complex for mathematical solutions.
D) It can be used for a wide range of applications.
E) It simplifies the design of operational processes.

Accepted Answer

Simulation may not necessarily simplify the design of operational processes, as it can sometimes be a complex process itself. However, it can help in optimizing and improving existing processes by identifying potential issues and testing out different scenarios.

Question 5

Natural logarithms are used in simulating the:
A) binomial distribution.
B) exponential distribution.
C) normal distribution.
D) Poisson distribution.
E) uniform distribution.

Accepted Answer

Natural logarithms are commonly used in simulating the exponential distribution because the distribution itself involves natural logarithms. Specifically, the probability density function of the exponential distribution involves the term e raised to the power of a negative value times x, where e is the natural logarithm base. Therefore, when simulating data from an exponential distribution, it is common to use natural logarithms in the process.

Question 6

An analyst wants to simulate observations from a Normal distribution that has a mean of 41 and a standard deviation of 3.The analyst draws a random number from a normally distributed table of random numbers.The random number is -2.00.The simulated value is:
A) 31
B) 35
C) 38
D) 43
E) none of the choices are correct.

Accepted Answer

The answer of An analyst wants to simulate observations from...

Question 7

A Uniform distribution has end points of 450 and 500,which represent the time limits for a production operation.A manager wants to simulate two times from this distribution,and has obtained the numbers 44 and 10 from a two-digit random number table.Respectively,the two simulated times are:
A) 460 and 494.
B) 472 and 455.
C) 455 and 472.
D) 494 and 460.
E) none of the choices are correct.

Accepted Answer

The random numbers 44 and 10 are converted to the uniform distribution range [450, 500] using the formula: simulated time = 450 + (random number/100) * (500 - 450). This gives 472 for 44 and 455 for 10.

Question 8

The number of machine breakdowns per day in a large factory can be described by a Poisson distribution with a mean of 2.0.Simulate the number of breakdowns over a five-day period,using these random numbers:

Accepted Answer

The answer of The number of machine breakdowns per day...

Question 9

Which statement does not accurately describe simulation?
A) Enables decision makers to conduct experiments
B) Involves developing models of processes
C) Alternatives are considered based on the what-if approach
D) Determines optimal solutions
E) Is a descriptive technique that does not produce a solution per se

Accepted Answer

Simulation can help decision makers evaluate different options or alternatives, but it does not necessarily determine the optimal solution. The goal of simulation is to provide insights and information about how a system or process operates under different conditions, which can inform decision making.

Question 10

An analyst wants to simulate observations from a Uniform distribution that has a lower limit of 60 minutes and an upper limit of 80 minutes.The analyst draws the random number 75 from a two-digit random number table.In terms of this uniform distribution,this is equivalent to a simulated value of:
A) 61
B) 65
C) 70
D) 75
E) none of the choices are correct.

Accepted Answer

The random number 75 falls within the range of the uniform distribution (60 to 80 minutes), so it directly corresponds to a simulated value of 75.

Question 11

Monte Carlo simulation is always associated with:
A) computers.
B) multiple-decision criteria.
C) gambling.
D) chance or random components.
E) a town in southern Italy.

Accepted Answer

The answer of Monte Carlo simulation is always associated with:
A)...

Question 12

A Normal distribution has a mean of 500 and a standard deviation of 50.A manager wants to simulate two values from this distribution,and has drawn these random numbers: -0.60 and +1.40.Respectively,the two values are:
A) 640 and 440.
B) 470 and 570.
C) 570 and 470.
D) 440 and 640.
E) none of the choices are correct.

Accepted Answer

To simulate a value from a normal distribution, we use the formula:

X = μ + σZ

Where X is the simulated value, μ is the mean of the normal distribution, σ is the standard deviation of the normal distribution, and Z is a standard normal random variable (i.e., a random variable with a mean of 0 and a standard deviation of 1).

For the first value, we have:

X = 500 + 50(-0.6) = 470

For the second value, we have:

X = 500 + 50(1.4) = 570

Therefore, the two values are 470 and 570, which corresponds to choice B.

Question 13

During a cross-country trip,a statistics professor decided that the probability that her car could break down on any day was .15.Assume a maximum of one breakdown per day.Repair time,she decided,was normally distributed with a mean of four hours and a standard deviation of .6 hours.Simulate 10 days using these random numbers:
  Simulate whether a breakdown would occur and,if so,time of repair.

Accepted Answer

The answer of During a cross-country trip,a statistics professor decided...

Question 14

Which of the following words does not characterize Monte Carlo?
A) Random
B) Chance
C) Sampling
D) Probabilistic
E) Deterministic

Accepted Answer

Monte Carlo is based on randomness, chance, sampling, and probabilities, so options A, B, C, and D all describe it accurately. Option E, deterministic, does not characterize Monte Carlo as it involves randomness and probability analysis.

Question 15

The second step in the simulation process is to:
A) run the simulation.
B) develop the simulation experiment(s).
C) test the simulation model.
D) develop the simulation model.
E) identify the problem and set objectives.

Accepted Answer

After identifying the problem and setting objectives, the next step is to develop the simulation model. Only after the model is developed can the simulation be tested and the experiments run.

Question 16

An item of inventory is checked at the end of each hour.Given the following data:
  Simulate 10 hours of operation for demand,beginning and ending inventories,and order placements and arrivals.Use the following random digits (left to right):

Accepted Answer

The answer of An item of inventory is checked at...

Question 17

The random numbers used in Monte Carlo simulations come from: I)any source II)computer generated numbers III)a table of random numbers
A) I only
B) II only
C) III only
D) II or III
E) I, II, or III

Accepted Answer

The random numbers used in Monte Carlo simulations can come from computer-generated numbers or a table of random numbers. While any source could theoretically be used, computer-generated numbers and tables of random numbers are preferred since they ensure true randomness and avoid any potential biases or patterns. Therefore, the best choice is either II or III.

Question 18

A production operation consists of two steps.The time for the first step is uniformly distributed between 10 minutes and 20 minutes.The time for the second operation is uniformly distributed between 15 and 20 minutes.Process one cannot start a new unit until its previous unit has been passed to process two.Process two cannot accept another unit while still processing the previous one.Using these two random number strings (left to right),simulate the total time for three units:

Accepted Answer

The answer of A production operation consists of two steps.The...

Question 19

Simulation is basically a technique which is used for:
A) optimizing.
B) testing solutions.
C) cost minimizing.
D) using random numbers.
E) heuristic problem solving.

Accepted Answer

Simulation is mainly used for testing solutions. It involves creating a hypothetical scenario of a real-life situation and testing different solutions and strategies to see which ones are most effective. This helps in identifying potential problems and finding solutions to them before implementing them in real life. Therefore, option B is the most appropriate choice. While simulation may involve the use of random numbers, it is not its sole purpose or technique. Options A, C, and E are also applicable to various techniques used in decision-making but do not define simulation.

Question 20

A Uniform distribution has endpoints of 250 and 400.Simulate three values of this distribution using these random numbers:

Accepted Answer

The answer of A Uniform distribution has endpoints of 250...

Quiz 18: B: Waiting-Line Analysis

Which of the following is not a reason for simulation's popularity?

Natural logarithms are used in simulating the:

An analyst wants to simulate observations from a Normal distribution that has a mean of 41 and a standard deviation of 3.The analyst draws a random number from a normally distributed table of random numbers.The random number is -2.00.The simulated value is:

A Uniform distribution has end points of 450 and 500,which represent the time limits for a production operation.A manager wants to simulate two times from this distribution,and has obtained the numbers 44 and 10 from a two-digit random number table.Respectively,the two simulated times are:

The number of machine breakdowns per day in a large factory can be described by a Poisson distribution with a mean of 2.0.Simulate the number of breakdowns over a five-day period,using these random numbers:

Which statement does not accurately describe simulation?

An analyst wants to simulate observations from a Uniform distribution that has a lower limit of 60 minutes and an upper limit of 80 minutes.The analyst draws the random number 75 from a two-digit random number table.In terms of this uniform distribution,this is equivalent to a simulated value of:

Monte Carlo simulation is always associated with:

A Normal distribution has a mean of 500 and a standard deviation of 50.A manager wants to simulate two values from this distribution,and has drawn these random numbers: -0.60 and +1.40.Respectively,the two values are:

Which of the following words does not characterize Monte Carlo?

The second step in the simulation process is to:

An item of inventory is checked at the end of each hour.Given the following data: Simulate 10 hours of operation for demand,beginning and ending inventories,and order placements and arrivals.Use the following random digits (left to right):

The random numbers used in Monte Carlo simulations come from: I) any source II) computer generated numbers III) a table of random numbers

Simulation is basically a technique which is used for:

A Uniform distribution has endpoints of 250 and 400.Simulate three values of this distribution using these random numbers: