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 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.

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

_________ 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 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	00-14
6	15-44
7	45-69
8	70-84
9	85-99

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 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.

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 :