A 100(1-α)% confidence interval for the population mean μ based on a sample of size
n with a sample mean ̅and a known population standard deviation σ is given by
________
A) za/2(n-1)( )
B)
C) x1 – / (σ / )
D) ̅ za/2(σ / √ )
Which of the following is true of a training data set?
A) They are primarily used to fine-tune models.
B) They provide the most realistic estimate for a model’s performance.
C) They are used to build models where the data is unknown.
D) They have known outcomes.
When using the t-statistic in multiple regression to determine if a variable should be
removed:
A) R2 will increase if the variable is removed.
B) if |t| > 1, the standard error will decrease.
C) a large number of independent variables is convenient.
D) if |t| < 1, the standard error will increase.
________ are statistical errors that are due to the sample not representing the target
population adequately.
A) Parallax errors
B) Sampling errors
C) Nonsampling errors
D) Quantization errors
Pickson Luthiers Corporation is studying where to locate a phone charging point on the
factory floor. The locations of five production cells are expressed as X– and
Y-coordinates on a rectangular grid of the factory layout. The daily demand for the
charging point (measured as the number of trips to the charging point) at each
production cell is also known. Because of the nature of the equipment layout in the
factory and for safety reasons, workers must travel along marked horizontal and vertical
aisles to access the charger. Thus, the distance from a cell to the charger is measured as
rectilinear distance.
The table below provides the relevant information.
The optimal location should minimize the total weighted distance between the charging
point and all production cells, where the weights are the daily number of trips to the
phone charging point.
According to the model, which of the following is the weighted distance between the
phone charger and Packaging cell?
A) 10.50
B) 0
C) 7.00
D) 14.00
Qualis Investments is a private limited business that manages personal financial
portfolios. The company manages six mutual funds and has a client that has acquired
$750,000 from an inheritance. Characteristics of the funds are given in the table below.
The company recommends that no more than $300,000 be invested in any individual
fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage
fund. The total amount invested in the low-priced and multinational funds are at least
35% of the total investment. The client would like an average return of at least 6%.
Assume that X1- X6 represent the dollar amounts invested in funds 1 through 6,
respectively.
Which of the following describes the constraint on the mid-cap fund?
A) X3 ≥ 0.35(750,000)
B) X3 ≥ 80,000
C) X3 ≥ 0.35(80,000)
D) X3 ≤ 670,000
The Risk Solver Platform ________ chart shows the minimum, first quartile, median,
third quartile, and maximum values in a data set graphically.
A) trend
B) sensitivity
C) overlay
D) box-whisker
Which of the following is the equation used for computing the sample correlation
coefficient?
A) rxy = cov(X,Y)(sxsy)
B) rxy = cov(X,Y)/SxSy
C) rxy =
D) rxy =
Below is a spreadsheet for a hotel overbooking model.
Assume that each reservation has a constant probability p = 0.04 of being cancelled.
Answer the question(s) using the Risk Solver Platform.
Which of the following cells is defined as an output cell?
A) B13
B) B14
C) B15
D) B17
The binominal distribution:
A) is a discrete distribution used to model the number of occurrences in some unit of
measure.
B) assumes that the average number of occurrences per unit is a constant and that
occurrences are independent.
C) is symmetric irrespective of the value of the probability of success.
D) models n independent replications of a Bernoulli experiment, each with a probability
p of success.
Which of the following approaches provided by the Analytic Solver Platform can
automatically run multiple optimizations while varying model parameters within a
predefined range?
A) sensitivity analysis
B) breakdown analysis
C) parameter analysis
D) uncertainty analysis
The exponential distribution:
A) has the density function f (x) = e-λx , for x ≥ 0.
B) models the time between randomly occurring events.
C) has an expected value λ.
D) is described by the familiar bell-shaped curve.
An unbounded problem is one for which ________.
A) the objective is maximized or minimized by more than one combination of decision
variables
B) there is no solution that simultaneously satisfies all the constraints
C) the objective can be increased or decreased to infinity or negative infinity while the
solution remains feasible
D) there is exactly one solution that will result in the maximum or minimum objective
Below is a payoff table that lists three mortgage options:
What is the maximum opportunity loss incurred for the 25-year fixed decision?
A) $ 8,626
B) $ 13,716
C) $ 14,369
D) $ 10,581
In an event X, the probability of rolling a sum of 8 on two dice is 5/36 while the
probability of
rolling an 11 is 2/36. In another event Y, the probability of rolling a 2 is 1/36, the
probability of
rolling a 9 is 4/36, and the probability of rolling a 4 is 3/36.
What is probability that neither X nor Y will occur?
A) 29/26
B) 1/36
C) 28/36
D) 21/36
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails,
rivets, and clips-which are machined on two CNC machining centers. The machining
centers have a capacity of 250,000 minutes per year. The gross margin per unit and
machining requirements are shown in the spreadsheet below.
What is the total profit generated from the manufacture of rivets?
A) $ 66,666.67
B) $ 100,000.00
C) $ 183,333.33
D) $ 150,000.00
When will a company use a predictive decision model?
A) when it wishes to determine the best product pricing to maximize revenue
B) when it wishes to know how best to use advertising strategies to influence sales
C) when it wishes to know sales patterns to plan inventory levels
D) when it wishes to ensure that a specified level of customer service is achieved
Calculate the median for the cost per order data.
A) $325
B) $154
C) $174.17
D) $88
If a data set has ‘c’ number of observations, the relative frequency of category ‘l’ is
computed as ________.
A) (frequency of category ‘l’) / ‘c’
B) ‘c’ (number of observations in category ‘l’)
C) (sum of all observations in category ‘l’) / ‘c’
D) sum of (‘c’ + each observation in category ‘l’)
In a two-sample test for differences in means, the hypotheses are of the form:
A)
B)
C)
D)
Stone Age Surfboards is a small manufacturer of two types of popular low-tide
surfboards, the Graystone and the Lava models. The manufacturing process consists of
two departments: fabrication and finishing. The fabrication department has 8 skilled
workers, each of whom works 9.25 hours per day. The finishing department has 5
workers, each of whom works a 6 -hour shift per day. Each pair of Graystone
surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in
finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in
finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the
Graystone model and $60 on the Lava model. The company anticipates selling at least
twice as many Lava models as Graystone models.
If the unit profit on Graystone surfboards is increased by $10, what is the shadow price
for the finishing hours used?
A) $18.48
B) $17.39
C) $15.42
D) $14.15
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues.
They have three classes of tickets: Classic, Silver, and Gold. The table below provides
information on the average ticket sales, revenue and price elasticity on demand. They
have a total seating capacity of 300. The table also provides the price range within
which they plan to reduce their ticket rates.
According to the nonlinear model, what is the new price for Classic tickets?
A) $7.50
B) $12.45
C) $6.50
D) $8.20
Below is the table showing rate of shoes sold per day and the highest-priced shoe sold
that day for a one-week period. The rate of shoes sold per day (X) and the price of the
shoes (Y).
Use Excel to calculate the z-score of X observation 27.
A) -0.24
B) 0
C) 0.18
D) 1.46
Which of the following characterizes a continuous random variable for which all
outcomes between some minimum and maximum value are equally likely?
A) exponential distribution
B) uniform distribution
C) normal distribution
D) lognormal distribution
Explain how the Markowitz portfolio model is a quadratic optimization model.
Calculate the economic value of a loyal customer for a company given that the
customer purchases, on an average, worth $43worth per visit and comes three times a
year. The company’s gross profit margin is 35 per cent with a customer defection rate of
0.4.
List the systematic approach to build good multiple regression models.
P(P|Q) = P(Q) – P(P or Q)
The table below shows the sales per day at a grocery store over a period of a week.
Calculate the z-score for sales on Day 4.
What is a job-sequencing problem? How can we find an optimal solution for such
problems?
Below is a decision tree illustrating the R&D process for a new drug.
Let us assume that if market is large, payoff is lognormally distributed with a mean of
$4,900 million and a standard deviation of $1,000 million; if market is medium, payoff
is lognormally distributed with a mean of $2,500 million and a standard deviation of
$500 million; and if market is small, payoff is normally distributed with a mean of
$1,800 million and standard deviation of $200 million. Let us also assume that the cost
of clinical trials is uncertain and estimates are modeled with a triangular distribution
with a minimum of -$ 700 million, a most likely value of – $550 million, and a
maximum of -$500 million. Use 10,000 trials and a random seed of 1.