MAT 540 MIDTERM (Week 5)

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

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

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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.

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

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5.      A table of random numbers must be normally distributed and efficiently generated.

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6.      Starting conditions have no impact on the validity of a simulation model.

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7.      Data cannot exhibit both trend and cyclical patterns. 
 

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

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

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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?

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

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12.  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.
 

 
What is the probability of 2 or fewer breakdowns?

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13.  A seed value is a(n)

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14.  In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.

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15.  Random numbers generated by a __________ process instead of a __________ process are pseudorandom numbers.

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16.  Which of the following characteristics is exhibited by the data?

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

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

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19.  Which of the following characteristics is exhibited by the data?

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20.  __________ is the difference between the forecast and actual demand.

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21.  Consider the following demand and forecast.
 

 
If MAD = 2, what is the forecast for period 4?

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

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

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24.  __________ is absolute error as a percentage of demand.

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25.  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.

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26.  The drying rate in an industrial process is dependent on many factors and varies according to the following distribution. 
   

(Table)

         
Compute the mean drying time.  Use two places after the decimal.

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27.  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.

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28.  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 ________.

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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. 

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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?

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31.  Consider the following probability distribution: 

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?

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32.  Given the following data, compute the MAD for the forecast.
 
                        Year    Demand           Forecast

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

 
 
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.

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34.  The following sales data are available for 2003-2008.
 
            (Table)
 
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.

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35.  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.

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

 
Use exponential smoothing with α = .2 and the smoothed forecast for July is 32. Determine the smoothed forecast for August.

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37.  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.

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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.

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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. 

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40.  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.

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