ISDS Final Exam
What is the mean of x, given the exponential probability function a. 0.05 b. 100 c. 20 d. 2,000
20
__________ is the situation in which no solution to the linear programming problem satisfies all the constraints. a. Unboundedness b. Infeasibility c. Optimality d. Divisibility
Infeasibility
In a __________ distribution, a random variable can take any value in a specified range. a. relative frequency b. cumulative c. discrete probability d. continuous probability
continuous probability
The center of a normal curve is a. the mean of the distribution. b. equal to the standard deviation. c. always a positive number. d. always equal to zero.
the mean of the distribution.
A set of values for the random variables is called a(n) a. event. b. permutation. c. trial. d. combination.
trial.
Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive-thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability that it takes less than one minute to fill an order? a. 0.4866 b. 0.6321 c. 0.7769 d. 0.1813
0.4866
In the probability table below, which value is a marginal probability? Completed Obstacle Course Level No Yes Total Challenging 0.4 0.3 0.7 Easy 0.1 0.2 0.3 Total 0.5 0.5 1.0
0.5
What is the total area under the normal distribution curve? a. It must be calculated b. 1 c. It depends upon the mean and standard deviation d. 100
1
A survey of 100 random high school students finds that 85 students watched the Super Bowl, 25 students watched the Stanley Cup Finals, and 20 students watched both games. How many students did not watch either game? a. 10 b. 30 c. 15 d. 20
10
A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. How many steps would he have to take to make the cut for the top 5% for his distribution? a. 7,533 b. 10,000 c. 12,467 d. 8,078
12,467
The random variable X is known to be uniformly distributed between 2 and 12. Compute the standard deviation of X. a. 8.333 b. 12 c. 2.887 d. 3.464
2.887
Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability density function for the time it takes to fill an order?
2/3e
The number of minutes that Samantha waits to catch the bus is uniformly distributed between 0 and 15 minutes. What is the probability that Samantha has to wait less than 4.5 minutes to catch the bus? a. 20% b. 30% c. 10% d. 3%
30%
The profit realized by the sales of a particular item follows a normal distribution with a mean of $0.5 million per quarter and a standard deviation of $0.1 million per quarter. What percent of the quarters can be expected to see a profit of at least $0.5 million? a. 60% b. 40% c. 10% d. 50%
50%
The random variable X is known to be uniformly distributed between 2 and 12. Compute E(X), the expected value of the distribution. a. 6 b. 7 c. 4 d. 5
7
The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What value represents the 50th percentile of this distribution? a. 85 b. 75 c. 105 d. 95
75
The weekly demand for an item in a retail store follows a uniform distribution over the range 70 to 83. What would be the weekly demand if its corresponding computer-generated value is 0.5? a. 90.1 b. 76.5 c. 50.85 d. 83
76.5
A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes in a day is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. One day he took 13,000 steps. What was his percentile on that day? a. 95% b. 100% c. 97.7% d. 99.7%
97.7%
A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes in a day is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. What percent of the days does he exceed 13,000 steps? a. 5% b. 2.28% c. 97.72% d. 95%
97.72%
Which of the following functions computes a value such that 2.5% of the area under the standard normal distribution lies in the upper tail defined by this value? a. =NORM.S.INV(0.975) b. =NORM.S.INV(0.025) c. =NORM.S.INV(0.05) d. =NORM.S.INV(0.95)
=NORM.S.INV(0.975)
Which of the following Excel functions would generate random integers from 0 to 100? a. =RAND( ) b. =SUMIF(A1:A100, 100) c. =RANDBETWEEN(0, 100) d. =100*RAND( )
=RANDBETWEEN(0, 100)
Which of the following numbers cannot result from the Excel function =NORM.INV(RAND( ), 100, 10)? a. 115 b. 121 c. 99 d. All of these numbers can result from this Excel function.
All of these numbers can result from this Excel function.
Which of the following cannot be described by a discrete probability distribution? a. The cost of parts for manufacturing an item, where the parts can take on any value between $80 and $100. b. Sales of two medical devices in which Device A generates $35 per unit sold and will likely constitute 30% of the sales and Device B generates $50 per unit sold and will likely constitute 70% of the sales. c. The number of units produced in a given day, where 20% of the time 99 units are produced and 80% of the time 100 units are produced. d. The labor cost for manufacturing goods, where one-third of the units cost $10 in labor, one-third cost $15 in labor, and one-third cost $50 in labor.
Each simulation run provides only a sample of how the real system will operate
Which of the following is a disadvantage of using simulation? a. Experimenting directly with a simulation model is often not feasible. b. Simulation models warn against poor decision strategies by projecting disastrous outcomes such as system failures, large financial losses, and so on. c. The simulation models are used to describe systems without requiring the assumptions that are required by mathematical models. d. Each simulation run provides only a sample of how the real system will operate.
Each simulation run provides only a sample of how the real system will operate
In Excel, the expression LN(RAND())*(-m) would generate a(n) __________ random variable with mean m. a. lognormal b. logarithmic c. exponential d. normal
Exponential
A(n) ___________ solution satisfies all the constraint expressions simultaneously. a. objective b. feasible c. infeasible d. extreme
Feasible
Which statement is true about mutually exclusive events? a. If either event A or event B must occur, they are called mutually exclusive. b. P(A) + P(B) = 1 for any events A and B that are mutually exclusive. c. If events A and B cannot occur at the same time, they are called mutually exclusive. d. None of these choices are correct.
If events A and B cannot occur at the same time, they are called mutually exclusive.
Which of the following is true of verification? a. It requires an agreement among analysts and managers. b. It is performed prior to the development of the computer procedure for simulation. c. It deals with the accurate modeling of real system operations. d. It is largely a debugging task.
It is largely a debugging task.
A ___________ uses repeated random sampling to represent uncertainty in a model representing a real system and that computes the values of model outputs. a. Monte Carlo simulation b. deterministic model c. discrete event simulation d. what-if analysis
Monte Carlo simulation
For a given mean and standard deviation, the __________ function in Excel is used to generate a value for the random variable characterized by a normal distribution. a. VLOOKUP b. FREQUENCY c. RAND d. NORM.INV
NORM.INV
The __________ function in Excel is used to compute the statistics required to create a histogram. a. NORM.INV b. RAND c. FREQUENCY d. STDEV.S
NORM.INV
In a normal distribution, which is greater, the mean or the median? a. Mean b. Median c. Neither the mean or the median (they are equal) d. Cannot be determined with the information provided.
Neither the mean or the median (they are equal)
Which of the following cannot be modeled by a continuous distribution? a. Height of the finished manufactured product b. Number of products produced in an hour c. Length of time it takes to manufacture a product d. Weight of a finished manufactured product
Number of products produced in an hour
The __________ probability distribution can be used to estimate the number of vehicles that go through an intersection during the lunch hour. a. binomial b. triangular c. Poisson d. normal
Poisson
__________, or modeling, is the process of translating a verbal statement of a problem into a mathematical statement. a. Problem-solving approach b. Data preparation c. Data structuring d. Problem formulation
Problem formulation
The __________ assumption necessary for a linear programming model to be appropriate means that the contribution to the objective function and the amount of resources used in each constraint are in accordance to the value of each decision variable. a. negativity b. additivity c. divisibility d. proportionality
Proportionality
The __________ function is used to generate a pseudorandom number in Excel. a. FREQUENCY() b. ROUND() c. RAND() d. NORM.INV()
RAND()
The Excel function __________ generates integer values between lower and upper bounds. a. RANDBETWEEN b. UPPER c. LOWER d. RAND
RANDBETWEEN
Which of the following parameters is required to convert a computer-generated random variable into a uniform random variable? a. Mean of the distribution b. Range of the distribution c. Moments of the distribution d. Variance of the distribution
Range of the distribution
Suppose that profit for a particular product is calculated using the linear equation: Profit = 20S + 3D. Which of the following combinations of S and D would yield a maximum profit? a. S = 0, D = 299 b. S = 182, D = 145 c. S = 405, D = 0 d. S = 0, D = 0
S = 405, D = 0
Which algorithm, developed by George Dantzig and utilized by Excel Solver, is effective at investigating extreme points in an intelligent way to find the optimal solution to even very large linear programs? a. Ellipsoidal algorithm b. Trial-and-error algorithm c. Simplex algorithm d. Complex algorithm
Simplex algorithm
In reviewing the graph below, which of the following inferences can be drawn about the monthly salary? a. The monthly salary is always less than $3,000. b. The range of the monthly salary distribution is $3,000 to $5,000. c. The average monthly salary is $3,000. d. The monthly salary is always greater than $3,000.
The average monthly salary is $3,000.
Which of the following statements is correct? a. The binomial and normal distributions are both continuous probability distributions. b. The binomial distribution is a continuous probability distribution, and the normal distribution is a discrete probability distribution. c. The binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution. d. The binomial and normal distributions are both discrete probability distributions.
The binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution.
Which of the following is a discrete random variable? a. The amount of gasoline purchased by a customer b. The height of water-oak trees c. The amount of mercury found in fish caught in the Gulf of Mexico d. The number of times a student guesses the answers to questions on a certain test
The number of times a student guesses the answers to questions on a certain test
Which of the following is not a characteristic of the normal probability distribution? a. The mean of the distribution can be negative, zero, or positive. b. The standard deviation must be 1. c. The mean, median, and the mode are equal. d. The distribution is symmetrical.
The standard deviation must be 1.
Which of the following inferences about a variable of interest can be drawn from the graph given below? a. The variable is more likely to take the value 20 than 40. b. The variable is equally likely to take any value between 20 and 40. c. The variable can only take the value 30. d. The variable is more likely to take any value outside the range of 20 and 40.
The variable is more likely to take any value outside the range of 20 and 40.
The situation in which the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraints is known as a. semi-optimality. b. unbounded. c. infiniteness. d. infeasibility.
Unbounded
The time it takes to manufacture a product is modeled by a continuous distribution. The time to manufacture one unit can take anywhere from 5 to 6 minutes with equal probability. What distribution can be used to model the random variable, production time? a. Discrete probability distribution b. Binomial distribution c. Normal distribution d. Uniform distribution
Uniform distribution
__________ is the process of determining that a simulation model provides an accurate representation of a real system. a. Validation b. Verification c. Consideration d. Regression
Validation
The range of computer-generated random numbers is a. [-8, 0). b. [1, 8]. c. [-8, 8]. d. [0, 1).
[0, 1).
The assumption that is necessary for a linear programming model to be appropriate and that ensures that the value of the objective function and the total resources used can be found by summing the objective function contribution and the resources used for all decision variables is known as a. proportionality. b. divisibility. c. additivity. d. negativity.
additivity.
A scenario in which the optimal objective function contour line coincides with one of the binding constraint lines on the boundary of the feasible region leads to __________ solutions. a. binding b. infeasible c. unique optimal d. alternative optimal
alternative optimal
The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What is the probability that, if driven normally, the car will get 100 miles per gallon or better? a. 25% b. 0.6% c. 2.5% d. 6%
b. 0.6%
Two events are independent if a. the probability of one or both events is greater than 1. b. P(A | B) = P(A) or P(B | A) = P(B). c. the two events occur at the same time. d. None of these choices are correct.
b. P(A | B) = P(A) or P(B | A) = P(B).
A __________ refers to a constraint that can be expressed as an equality at the optimal solution. a. nonnegativity constraint b. first class constraint c. binding constraint d. slack variable
binding constraint
An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a a. discrete random variable. b. categorical random variable. c. continuous random variable. d. complex random variable.
continuous random variable
An input to a simulation model that is selected by the decision maker is known as a a. controllable input. b. probable input. c. random variable. d. nonnegativity constraint.
controllable input
A controllable input for a linear programming model is known as a a. dummy variable. b. constraint. c. parameter. d. decision variable.
decision variable.
A variable that can only take on specific numeric values is called a a. discrete random variable. b. categorical variable. c. continuous random variable. d. complex random variable.
discrete random variable.
The random variables corresponding to the interarrival times of customers and the service times of the servers are commonly part of a(n) __________ simulation. a. what-if b. risk analysis c. discrete-event d. Monte Carlo
discrete-event
In a linear programming model, the __________ assumption plus the nonnegativity constraints mean that decision variables can take on any value greater than or equal to zero. a. divisibility b. additivity c. negativity d. proportionality
divisibility
Bayes' theorem is a method used to compute __________ probabilities. a. empirical b. posterior c. conditional d. prior
empirical
The points where constraints intersect on the boundary of the feasible region are termed as the a. feasible points. b. feasible edges. c. extreme points. d. objective function contour.
extreme points.
The values for random variables in a Monte Carlo simulation are a. selected manually. b. taken from forecasting analysis. c. derived secondarily using formulas. d. generated randomly from probability distributions.
generated randomly from probability distributions.
The choice of the probability distribution for a random variable can be guided by a. an objective function. b. historical data. c. forecasting. d. likelihood factors.
historical data.
A mathematical function in which each variable appears in a separate term and is raised to the first power is known as a a. linear function. b. power function. c. what-if function. d. nonlinear function.
linear function.
If a z-score is zero, then the corresponding x-value must be equal to the a. mode. b. mean. c. standard deviation. d. median.
mean.
A distribution of a random variable for which values extremely larger or smaller than the mean are increasingly unlikely can possibly be modeled as a(n) _____________ probability distribution. a. binomial b. normal c. gamma d. exponential
normal
The type of distribution shown in the graph below is a(n) __________ distribution. a. exponential b. beta c. normal d. uniform
normal
Probability is the a. number of successes divided by the standard deviation of the distribution. b. number of successes divided by the number of failures. c. numerical measure of the likelihood that an event will occur. d. chance that an event will not happen.
numerical measure of the likelihood that an event will occur.
The term __________ refers to the expression that defines the quantity to be maximized or minimized in a linear programming model. a. problem formulation b. objective function c. decision variable d. association rule
objective function
A(n) __________ refers to a set of points that yield a fixed value of the objective function. a. objective function contour b. infeasible solution c. objective function coefficient d. feasible region
objective function contour
In problem formulation, the a. objective is expressed in terms of the decision variables. b. constraints are expressed in terms of the obtained objective function coefficients. c. optimal solution is decided upon. d. nonnegativity constraints are always ignored.
objective is expressed in terms of the decision variables.
Geometrically, binding constraints intersect to form the a. zero slack. b. subspace. c. optimal point. d. decision cell.
optimal point.
An initial estimate of the probabilities of events is a __________ probability. a. empirical b. posterior c. conditional d. prior
prior
A __________ describes the range and relative likelihood of all possible values for a random variable. a. probability mass function of an event b. probability distribution for a random variable c. probability d. density function
probability distribution for a random variable
The outcome of a simulation experiment is a(n) a. probability distribution for one or more output measures. b. objective function. c. single number. d. what-if scenario.
probability distribution for one or more output measures.
A description of the range and relative likelihood of possible values of an uncertain variable is known as a a. simulation optimization. b. base-case scenario. c. risk analysis. d. probability distribution.
probability distribution.
In simulation analysis, the ___________ of random variables can be adjusted to determine the impact of the assumptions about the shape of the uncertainty on the results. a. probability distributions b. relative frequencies c. ranges d. manual generations
probability distributions
A joint probability is the a. sum of the probabilities of two events. b. sum of the probabilities of two independent events. c. probability of the intersection of two events. d. probability of the union of two events.
probability of the intersection of two events.
A(n) __________ is an input to a simulation model whose value is uncertain and described by a probability distribution. a. random variable b. constraint c. decision variable d. identifier
random variable
A simulation model extends spreadsheet modeling by a. using historical data to make predictions about future values and expected trends. b. extending the range of parameters for which solutions are computed. c. using real-time values for parameters from the application to formulate solutions. d. replacing the use of single values for parameters with a range of possible values.
replacing the use of single values for parameters with a range of possible values.
Constraints are a. quantities to be minimized in a linear programming model. b. restrictions that limit the settings of the decision variables. c. quantities to be maximized in a linear programming model. d. input variables that can be controlled during optimization.
restrictions that limit the settings of the decision variables.
The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as a. decision tree analysis. b. regression analysis. c. risk analysis. d. data mining.
risk analysis.
The triangular distribution is a good model for __________ distributions. a. poisson b. uniform c. normal d. skewed
skewed
The __________ value for each less-than-or-equal-to constraint indicates the difference between the left-hand and right-hand values for a constraint. a. slack b. unbounded c. surplus d. objective function coefficient
slack
A variable subtracted from the left-hand side of a greater-than-or-equal to constraint to convert the constraint into an equality is known as a(n) a. unbounded variable. b. binding constraint. c. surplus variable. d. slack variable.
surplus variable.
Sample space is a. the collection of events b. a process that results in some outcome. c. a subgroup of a population/the likelihood of an outcome. d. the collection of all possible outcomes.
the collection of all possible outcomes.
All the events in the sample space that are not part of the specified event are called a. independent events. b. joint events. c. simple events. d. the complement of the event.
the complement of the event.
In a base-case scenario, the output is determined by assuming a. worst values that can be expected for the random variables of a model. b. best values that can be expected for the random variables of a model. c. the most likely values for the random variables of a model. d. the mean trial values for the random variables of a model.
the most likely values for the random variables of a model.
Nonnegativity constraints ensure that a. the problem modeling includes only nonnegative values in the constraints. b. the objective function of the problem always returns maximum quantities. c. there are no inequalities in the constraints. d. the solution to the problem will contain only nonnegative values for the decision variables.
the solution to the problem will contain only nonnegative values for the decision variables.
When formulating a constraint, care must be taken to ensure that a. there are no inequalities in the mathematical expression. b. the decision variables are set at either maximum or minimum values. c. all the objective function coefficients are included. d. the units of measurement on both sides of the constraint match.
the units of measurement on both sides of the constraint match.
A disadvantage of the simple what-if analyses is that a. there is no indication of the likelihood of various output values. b. the optimal solutions are not guaranteed. c. there are errors induced as a result of rounding. d. it cannot compute alternate optimal solutions.
there is no indication of the likelihood of various output values.
All of the following are examples of discrete random variables except a. marital status. b. time. c. number of tickets sold. d. population of a city.
time.
Problems with infeasible solutions arise in practice because a. of errors in objective function formulation. b. too many restrictions have been placed on the problem. c. management doesn't specify enough restrictions. d. there are too few decision variables.
too many restrictions have been placed on the problem.
All the values of computer-generated random numbers are a. uniformly distributed. b. lognormally distributed. c. Poisson distributed. d. normally distributed.
uniformly distributed.
The event containing the outcomes belonging to A or B or both is the __________ of A and B. a. intersection b. union c. Venn diagram d. complement
union
The process of determining that a computer program implements a simulation model as it is intended is known as a. verification. b. correlation. c. optimization. d. validation.
verification.
A __________ analysis involves considering alternative values for the random variables and computing the resulting value for the output. a. random b. risk c. what-if d. cluster
what-if
The slack value for binding constraints is a. zero. b. a negative integer. c. always a positive integer. d. equal to the sum of the optimal points in the solution.
zero.
