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Course Quantitative Methods

Test Midterm Exam

Question 1

Deterministic techniques assume that no uncertainty exists in model parameters.

Question 2

A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.

Question 3

A continuous random variable may assume only integer values within a given interval.

Question 4

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

Question 5

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

Question 6

Excel can only be used to simulate systems that can be represented by continuous random variables.

Question 7

The Delphi develops a consensus forecast about what will occur in the future.

Question 8

Data cannot exhibit both trend and cyclical patterns.

Question 9

A company markets educational software products, and is ready to place three new products on the market. Past experience has shown that for this particular software, the chance of “success” is 80%. Assume that the probability of success is independent for each product. What is the probability that exactly 1 of the 3 products is successful?

Question 10

__________ is a measure of dispersion of random variable values about the expected value.

Question 11

The __________ is the maximum amount a decision maker would pay for additional information.

Question 12

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?

Question 13

In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.

Question 14

Developing the cumulative probability distribution helps to determine

Question 15

A seed value is a(n)

Question 16

__________ is a linear regression model relating demand to time

Question 17

__________ methods are the most common type of forecasting method for the long-term strategic planning process.

Question 18

__________ is absolute error as a percentage of demand.

Question 19

Coefficient of determination is the percentage of the variation in the __________ variable that results from the __________ variable.

Question 20

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?

Question 21

Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

Question 22

Which of the following possible values of alpha would cause exponential smoothing to respond the most slowly to sudden changes in forecast errors?

Question 23

__________ is the difference between the forecast and actual demand.

Question 24

__________ is a category of statistical techniques that uses historical data to predict future behavior.

Question 25

An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as a table or a graph, both shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.

xi 0 1 2 3 4 5 6

p(xi) .10 .15 .18 .20 .20 .10 .07

What is the average number of complaints received per week? Round your answer to two places after the decimal.

Question 26

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.

Question 27

An 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 ________.

Question 28

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.

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 thinks the chances of low, medium, and high compliance are 20%, 30%, and 50% respectively, what is the expected value of perfect information? Note: Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if necessary.

Question 30

Consider the following decision tree.

What is the expected value at node 4? Round your answer to the nearest whole number. Do not include the dollar sign “$” in your answer.

Question 31

A normal distribution has a mean of 500 and a standard deviation of 50. A manager wants to simulate one value from this distribution, and has drawn the number 1.4 randomly. What is the simulated value?

Question 32

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 6. Use two places after the decimal.

Question 33

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.

Question 34

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.

Question 35

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.

Question 36

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.

Question 37

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

If the forecasted demand for June, July and August is 32, 38 and 42, respectively, what is MAPD? Write your answer in decimal form and not in percentages. For example, 15% should be written as 0.15. Use three significant digits after the decimal.

Question 38

Consider the following annual sales data for 2001-2008.

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.

Question 39

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.

Question 40

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.

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