MAT 540 WEEK 5 MIDTERM 1

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MAT 540 Week 5 Midterm 1

1.     Deterministic techniques assume that no uncertainty exists in model parameters. 

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

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

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

5.     Simulation results will always equal analytical results if 30 trials of the simulation have been conducted.

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

7.     Data cannot exhibit both trend and cyclical patterns. 

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

9.     In Bayesian analysis, additional information is used to alter the __________ probability of the occurrence of an event.

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

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

12.   Developing the cumulative probability distribution helps to determine

13.   A seed value is a(n)

14.   Pseudorandom numbers exhibit __________ in order to be considered truly random.

15.   Consider the following frequency of demand:



If the simulation begins with 0.8102, the simulated value for demand would be

16.   __________ is a linear regression model relating demand to time.

17.   rob
14, and 15)estion worth 2 points, 1 hour time limit (chapters 1,ue units EXCEPT:The U.S. Department of Agriculture estimates that the yearly yield of limes per acre is distributed as follows: 

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

19.   In exponential smoothing, the closer alpha is to __________, the greater the reaction to the most recent demand.

20.   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.

21.   Consider the following graph of sales.



Which of the following characteristics is exhibited by the data?

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

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

24.   Consider the following demand and forecast.

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. 

26.   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 ________.

27.   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.

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.

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?

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?

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?

32.   Consider the following annual sales data for 2001-2008.

33.   The following data summarizes the historical demand for a product.

34.   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. 

35.   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.

36.   Given the following data, compute the MAD for the forecast.

Year Demand Forecast 

37.   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.

38.   The following sales data are available for 2003-2008 : 

39.   The following data summarizes the historical demand for a product 

40.   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.