MAT 540 Midterm Exam by xuyuzhu

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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.

								
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