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MAT 540 Midterm Exam: 1. Deterministic techniques assume that no uncertainty exists in model parameters. Answer True False 5 points Question 2 1. A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously. Answer True False 5 points Question 3 1. 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 5 points Question 4 1. A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches. Answer True False 5 points Question 5 1. A table of random numbers must be normally distributed and efficiently generated. Answer True False 5 points Question 6 1. Excel can only be used to simulate systems that can be represented by continuous random variables. Answer True False 5 points Question 7 1. Qualitative methods are the least common type of forecasting method for the long-term strategic planning process. Answer True False 5 points Question 8 1. Data cannot exhibit both trend and cyclical patterns. Answer True False 5 points Question 9 1. In Bayesian analysis, additional information is used to alter the __________ probability of the occurrence of an event. Answer marginal conditional binomial revised 5 points Question 10 1. 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? Answer 0.80 0.032 0.24 0.096 5 points Question 11 1. The __________ is the maximum amount a decision maker would pay for additional information. Answer expected opportunity loss expected value expected value of perfect information none of the above 5 points Question 12 1. 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 Cumulative breakdowns Probability probability per week 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 5 points Question 13 1. Developing the cumulative probability distribution helps to determine Answer simulation numbers data sets random number ranges all of the above 5 points Question 14 1. Consider the following frequency of demand: If the simulation begins with 0.8102, the simulated value for demand would be Answer 1 2 3 4 5 points Question 15 1. In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution. Answer sampling from running integrating implementing 5 points Question 16 1. In exponential smoothing, the closer alpha is to __________, the greater the reaction to the most recent demand. Answer -1 0 1 -1 or 1 5 points Question 17 1. __________ is a measure of the strength of the relationship between independent and dependent variables. Answer Correlation Linear regression Coefficient of determination Regression 5 points Question 18 1. 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: Yield, bushels Probability per acre 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? Answer 425 442 440 475 5 points Question 19 1. __________ methods are the most common type of forecasting method for the long-term strategic planning process. Answer Regression Qualitative Time series all of the above 5 points Question 20 1. 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 .10 .50 .90 5 points Question 21 1. __________ is a category of statistical techniques that uses historical data to predict future behavior. Answer Qualitative methods Regression Time series Quantitative methods 5 points Question 22 1. 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 19 20 21 none of the above 5 points Question 23 1. 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 5 points Question 24 1. Coefficient of determination is the percentage of the variation in the __________ variable that results from the __________ variable. Answer dependent, dependent independent, dependent dependent, independent independent, independent 5 points Question 25 1. 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 5 points Question 26 1. 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. Answer 5 points Question 27 1. 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 5 points Question 28 1. 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 5 points Question 29 1. 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. Answer 5 points Question 30 1. 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 5 points Question 31 1. Consider the following distribution and random numbers: If a simulation begins with the first random number, what would the first simulation value would be __________. Answer 5 points Question 32 1. 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 5 points Question 33 1. Robert wants to know if there is a relation between money spent on gambling and winnings. What is the coefficient of determination? Use two significant places after the decimal. Answer 5 points Question 34 1. 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 5 points Question 35 1. Given the following data, compute the MAD for the forecast. Year Demand Forecast 2001 16 18 2002 20 19 2003 18 24 Answer 5 points Question 36 1. 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 5 points Question 37 1. 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. Answer 5 points Question 38 1. The following data summarizes the historical demand for a product. Actual Month 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 5 points Question 39 1. The following data summarizes the historical demand for a product Actual Month 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. Answer 5 points Question 40 1. 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.