MATH 540 MIDTERM (40 Questions)
MAT 540 MIDTERM
1. Deterministic techniques assume that no uncertainty exists in model parameters. Answer
True
False
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
3. A continuous random variable may assume only integer values within a given interval. Answer
True
False
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 longterm 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 zscore (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.
No. of breakdowns per week  Probability  Cumulative probability 
0  .10  .10 
1  .25  .35 
2  .36  .71 
3  .22  .93 
4  .07  1.00 
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 6period time frame:
If the forecast for period 5 is equal to 275, use exponential smoothing with α = .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
Period  Demand  Forecast 
1  7  10 
2  12  15 
3  18  20 
4  22  

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.
Demand  Random
Number Ranges 
5  0014 
6  1544 
7  4569 
8  7084 
9  8599 
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.
Month  Actual Demand 
March  20 
April  25 
May  40 
June  35 
July  30 
August  45 
Use exponential smoothing with α = .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 20012008.
Year  Sales 
2001  2 
2002  4 
2003  10 
2004  8 
2005  14 
2006  18 
2007  17 
2008  20 
Calculate the correlation coefficient . Use four significant digits after the decimal.
Answer
Question 36
The following sales data are available for 20032008. Determine a 4year 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 6period time frame: Compute a 3period 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 20032008 :
Year  Sales  Forecast 
2003  7  9 
2004  12  10 
2005  14  15 
2006  20  22 
2007  16  18 
2008  25  21 
Calculate the absolute value of the average error. Use three significant digits after the decimal.
Answer
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