MAT 540 MIDTERM SOLUTIONS (40/40)

Question
1
1. Deterministic
techniques assume that no uncertainty exists in model parameters.
Answer
True
False

Question
2
2.
An inspector correctly identifies defective products 90% of the time. For the
next 10 products, the probability that he makes fewer than 2 incorrect
inspections is 0.736.
Answer

True
False
Question
3
3.
A continuous random variable may assume only integer values within a given
interval.
Answer
True
False

Question
4
4.
A decision tree is a diagram consisting of circles decision nodes, square
probability nodes, and branches.
Answer

True
false
5. Question 5
Excel
can only be used to simulate systems that can be represented by continuous
random variables.
Answer

True
False

Question 6
Starting
conditions have no impact on the validity of a simulation model.
Answer

True
False

Question 7
Data
cannot exhibit both trend and cyclical patterns.
Answer
True
false
Question 8
Qualitative
methods are the least common type of forecasting method for the long-term
strategic planning process.
Answer

True
false
Question 9
Assume
that it takes a college student an average of 5 minutes to find a parking spot
in the main parking lot. Assume also that this time is normally distributed
with a standard deviation of 2 minutes. What time is exceeded by approximately
75% of the college students when trying to find a parking spot in the main
parking lot?
Answer

5.8
minutes
6.4
minutes
9.2
minutes
3.5
minutes
Question 10
__________
is a measure of dispersion of random variable values about the expected value.
Answer

Standard
deviation
Range
The
z-score (the standard score)
All
of the above
Question 11
The
__________ is the expected value of the regret for each decision.
Answer

expected
value
expected
opportunity loss
expected
value of perfect information
none
of the above
Question 12
Developing
the cumulative probability distribution helps to determine
Answer

the
coefficient of variation
data
sets
random
number ranges
all
of the above
Question 13
Two
hundred simulation runs were completed using the probability of a machine
breakdown from the table below. The average number of breakdowns from the
simulation trials was 1.93 with a standard deviation of 0.20.
What
is the probability of 2 or fewer breakdowns?
Answer

.10
.25
.35
.71
Question 14
Random
numbers generated by a __________ process instead of a __________ process are
pseudorandom numbers.
Answer

physical
/ physical
physical
/ mathematical
mathematical
/ physical.
mathematical
/ mathematical
Question 15
Consider
the following frequency of demand:
If
the simulation begins with 0.8102, the simulated value for demand would be
Answer

1
2
3
4
_________ is a category of statistical
techniques that uses historical data to predict future behavior.
Answer
Qualitative methods
Regression
Time series
Quantitative methods
Question 17
Given
the following data on the number of pints of ice cream sold at a local ice
cream store for a 6-period time frame:
If
the forecast for period 5 is equal to 275, use exponential smoothing with ? =
.40 to compute a forecast for period 7.
Answer

273
277
267.8
286.2
Question 18
Which
of the following possible values of alpha would cause exponential smoothing to
respond the most slowly to sudden changes in forecast errors?
Answer

.01
0.10
0.50
0.90
Question 19
__________
is the difference between the forecast and actual demand.
Answer

Forecast mistake
Forecast error
MAD
Forecast accuracy
Question 20
In exponential smoothing, the closer alpha is
to __________, the greater the reaction to the most recent demand.
Answer
-1
0
1
-1 or 1
Question 21
Consider
the following demand and forecast
If MAD = 2, what is the forecast for period
4?
Answer
21
22
23
None of the above
Question 22
__________
is absolute error as a percentage of demand
Cumulative
error
MAD
MAPD
Average
error
Question 23
Coefficient
of determination is the percentage of the variation in the __________ variable
that results from the __________ variable
dependent,
dependent
independent,
dependent
dependent,
independent
independent,
independent
Question 24
Consider
the following graph of sales
Which of the following characteristics is exhibited by
the data?
Answer
Trend only
Trend plus seasonal
Cyclical only
None of the above
Question 25
A
loaf of bread is normally distributed with a mean of 22 oz and a standard
deviation of 0.5 oz. What is the probability that a loaf is larger than 21 oz?
Round your answer to four places after the decimal
Answer
Question
26
A
life insurance company wants to estimate their annual payouts. Assume that the
probability distribution of the lifetimes of the participants is approximately
a normal distribution with a mean of 68 years and a standard deviation of 4
years. What proportion of the plan recipients would receive payments beyond age
75? Round your answer to four places after the decimal.
Answer
Question
27
online
sweepstakes has the following payoffs and probabilities. Each person is limited
to one entry.
The
probability of winning at least $1,000.00 is ________.
Answer
Question 28
A
fair die is rolled 8 times. What is the probability that an even number (2,4,
6) will occur between 2 and 4 times? Round your answer to four places after the
decimal
Answer
Question
29
The
local operations manager for the IRS must decide whether to hire 1, 2, or 3
temporary workers. He estimates that net revenues will vary with how well
taxpayers comply with the new tax code. The following payoff table is given in
thousands of dollars (e.g. 50 = $50,000).

If
he uses the maximin criterion, how many new workers will he hire?
Answer
Question 30
An
investor is considering 4 different opportunities, A, B, C, or D. The payoff
for each opportunity will depend on the economic conditions, represented in the
payoff table below.
Economic
Condition
Poor Average Good Excellent
Investment (S1) (S2) (S3) (S4)
A 50 75 20 30
B 80 15 40 50
C -100 300 -50 10
D 25 25 25 25
If
the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05
respectively, what is the highest expected payoff?
Answer
Question 31
Given
the following random number ranges and the following random number sequence:
62, 13, 25, 40, 86, 93, determine the average demand for the following
distribution of demand.
Answer
Question 32
Robert
wants to know if there is a relation between money spent on gambling and
winnings

What is the coefficient of determination? Note: please report your answer with
2 places after the decimal point.
Answer
Question 33
This
is the data from the last 4 weeks:
Use the equation of the regression line to forecast the increased sales for
when the number of ads is 10.
Answer
Question 34
The
following data summarizes the historical demand for a product.
Use
exponential smoothing with ? = .2 and the smoothed forecast for July is 32.
Determine the smoothed forecast for August.
Answer
Question 35
Consider
the following annual sales data for 2001-2008.
Calculate
the correlation coefficient . Use four significant digits after the decimal.
Answer
Question 36
The
following sales data are available for 2003-2008.

Determine a 4-year weighted moving average forecast for 2009, where weights are
W1 = 0.1, W2 = 0.2, W3 = 0.2 and W4 = 0.5.
answer
Question 37
Daily
highs in Sacramento for the past week (from least to most recent) were: 95,
102, 101, 96, 95, 90 and 92. Develop a forecast for today using a 2 day moving
average.
Answer
Question 38
Given
the following data on the number of pints of ice cream sold at a local ice
cream store for a 6-period time frame:
Compute a 3-period moving average for period 4. Use two places after the
decimal.
Answer
Question 39
Daily
highs in Sacramento for the past week (from least to most recent) were: 95,
102, 101, 96, 95, 90 and 92. Develop a forecast for today using a weighted
moving average, with weights of .6, .3 and .1, where the highest weights are
applied to the most recent data.
Answer
Question 40
The
following sales data are available for 2003-2008 :
Calculate
the absolute value of the average error. Use three significant digits after the
decimal.
Answer