MAT 540 Midterm Exam

1. Deterministic techniques assume that no uncertainty exists in model parameters
2. A continuous random variable may assume only integer values within a given interval.
3. A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.
4. A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches.
5. A table of random numbers must be normally distributed and efficiently generated.
6. Starting conditions have no impact on the validity of a simulation model.

7. The Delphi develops a consensus forecast about what will occur in the future
8. Qualitative methods are the least common type of forecasting method for the long-term strategic planning process.
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?
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. Consider the following frequency of demand: If the simulation begins with 0.8102, the simulated value for demand would be

14. Pseudorandom numbers exhibit __________ in order to be considered truly random.
15. 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?

16. The U.S. Department of Agriculture estimates that the yearly yield of limes per acre is distributed as follows:

Yield, bushels per acre            Probability
350                                          .10
400                                          .18
450                                          .50
500                                          .22
The estimated average price per bushel is $16.80. What is the expected yield of the crop?
17.  __________ is a linear regression model relating demand to time.
18. Consider the following graph of sales. Which of the following characteristics is exhibited by the data?
19. Consider the following graph of sales. Which of the following characteristics is exhibited by the data?
20. __________ is absolute error as a percentage of demand.
21.  __________ is a category of statistical techniques that uses historical data to predict future behavior.
22. Which of the following possible values of alpha would cause exponential smoothing to respond the most slowly to sudden changes in forecast errors?
23. __________ methods are the most common type of forecasting method for the long-term strategic planning process.
24. In exponential smoothing, the closer alpha is to __________, the greater the reaction to the most recent demand.

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.

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.

27. The drying rate in an industrial process is dependent on many factors and varies according to the following distribution. Compute the mean drying time. Use two places after the decimal.

28. 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.

29. 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?

30. 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?
31. Consider the following distribution and random numbers: If a simulation begins with the first random number, what would the first simulation value would be __________.
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.

33. 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.
34. The following sales data are available for 2003-2008 :   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.

35. 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.

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.
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.

38. 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.

39. 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.

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

Calculate the correlation coefficient. Use four significant digits after the decimal.