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MAT 540 Week 5 Midterm Exam (Latest)
Description
- 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. 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.
4. A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches
5. Starting conditions have no impact on the validity of a simulation model
6. A table of random numbers must be normally distributed and efficiently generated.
7. The Delphi develops a consensus forecast about what will occur in the future
8. Data cannot exhibit both trend and cyclical patterns
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. 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
11. The __________ is the expected value of the regret for each decision
12. In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution
13. Pseudorandom numbers exhibit __________ in order to be considered truly random.
14. Random numbers generated by a __________ process instead of a __________ process are pseudorandom numbers
15. Consider the following frequency of demand:
If the simulation begins with 0.8102, the simulated value for demand would be
16. Which of the following characteristics is exhibited by the data?
17. _______ is a linear regression model relating demand to time
18. _______ methods are the most common type of forecasting method for the long-term strategic planning process
19. Coefficient of determination is the percentage of the variation in the __________ variable that results from the __________ variable
20. ____________ is a measure of the strength of the relationship between independent and dependent variables.
21. ________ is a category of statistical techniques that uses historical data to predict future behaviour
22. __________ is absolute error as a percentage of demand.
23. __________ is the difference between the forecast and actual demand.
24. Which of the following possible values of alpha would cause exponential smoothing to respond the most slowly to sudden changes in forecast errors
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
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 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
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.
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 = $50,000). Round to the nearest whole number, if necessary.
30. Consider the following decision tree.
What is the expected value at node 4? Round your answer to the nearest whole number. Do not include the dollar sign “$” in your answer
31. Consider the following probability distribution:
Demand
Probability
0
0.15
1
0.30
2
0.25
3
0.15
4
0.15
Partition 100 numbers from 0 to 99 according to the probability of each demand value, starting with 0. A number from the 100 numbers is going to be
selected. What is the corresponding demand value if 62 is selected?
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. 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.
34. 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.
35. 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.
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. 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.
39. Given the following data, compute the MAD for the forecast.
Year Demand Forecast
2001
16
18
2002
20
19
2003
18
24
40. 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.