< Strayer MAT 540 Quantitative Methods Mid term Exam >

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Question 1                                                                                                                                          5 out of 5 points

 

 

 

 Deterministic techniques assume that no uncertainty exists in model parameters.

 

Question 2                                                                                                                                          5 out of 5 points

 

               

 

 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.

 

Question 3                                                                                                                                          5 out of 5 points

 

 A continuous random variable may assume only integer values within a given interval.

 

 Question 4                                                                                                                                         5 out of 5 points

 

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

 

Question 5                                                                                                                                          5 out of 5 points

 

 Simulation results will always equal analytical results if 30 trials of the simulation have been conducted.

 

Question 6                                                                                                                                          5 out of 5 points

 

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

 

Question 7                                                                                                                                          5 out of 5 points

 

 Qualitative methods are the least common type of forecasting method for the long-term strategic planning process.

 

Question 8                                                                                                                                          5 out of 5 points

 

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

 

Question 9                                                                                                                                          5 out of 5 points

 

 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?

 

 

 

 

 

 

 

Question 10                                                                                                                                       0 out of 5 points

 

               

 

 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?

 

Question 11                                                                                                                                       5 out of 5 points

 

 The __________ is the expected value of the regret for each decision.

 

Question 12                                                                                                                                       5 out of 5 points

 

 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?

 

Question 13                                                                                                                                       5 out of 5 points

 

 Consider the following frequency of demand:

 

If the simulation begins with 0.8102, the simulated value for demand would be

 

 

 

 

 

 

 

 

 

Question 14                                                                                                                                       5 out of 5 points

 

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

 

Question 15                                                                                                                                       5 out of 5 points

 

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

 

Question 16                                                                                                                                       5 out of 5 points

 

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

 

Question 17                                                                                                                                       5 out of 5 points

 

Consider the following graph of sales.

 

Which of the following characteristics is exhibited by the data?

 

Question 18                                                                                                                                       5 out of 5 points

 

__________ is the difference between the forecast and actual demand.

 

Question 19                                                                                                                                       5 out of 5 points

 

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

 

Question 20                                                                                                                                       5 out of 5 points

 

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?

 

 

 

 

 

 

 

 

 

Question 21                                                                                                                                       5 out of 5 points

 

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

 

Question 22                                                                                                                                       0 out of 5 points              

 

 __________ is a measure of the strength of the relationship between independent and dependent variables.

 

Question 23                                                                                                                                       5 out of 5 points

 

 Consider the following graph of sales.

 

Which of the following characteristics is exhibited by the data?

 

Question 24                                                                                                                                       5 out of 5 points

 

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

 

Question 25                                                                                                                                       5 out of 5 points

 

 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.

 

Question 26                                                                                                                                       5 out of 5 points

 

 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.

 

 

 

 

 

 

 

 

 

Question 27                                                                                                                                       5 out of 5 points

 

 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.

 

Question 28                                                                                                                                       5 out of 5 points

 

 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.

 

Question 29                                                                                                                                       0 out of 5 points

 

 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?

 

Question 30                                                                                                                                       5 out of 5 points

 

 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?

 

 

 

 

 

 

 

 

 

Question 31                                                                                                                                       5 out of 5 points

 

 A normal distribution has a mean of 500 and a standard deviation of 50. A manager wants to simulate one value from this distribution, and has drawn the number 1.4 randomly.  What is the simulated value?

 

                                               

 

Question 32                                                                                                                                       5 out of 5 points

 

 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.

 

 

 

Question 33                                                                                                                                       5 out of 5 points

 

 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.

 

 

 

Question 34                                                                                                                                       5 out of 5 points

 

 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.

 

 

 

 

 

 

 

 

 

 

 

 

 

Question 35                                                                                                                                       5 out of 5 points

 

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.

 

                                               

 

Question 36                                                                                                                                       5 out of 5 points

 

               

 

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.

 

Question 37                                                                                                                                       0 out of 5 points

 

Given the following data, compute the MAD for the forecast.

 

Year

Demand

Forecast

2001

16

18

2002

20

19

2003

18

24

 

 

 

Question 38                                                                                                                                       5 out of 5 points

 

 

 

 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.

 

 

 

Question 39                                                                                                                                       5 out of 5 points

 

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.

 

                                               

 

 

 

 

 

 

 

Question 40                                                                                                                                       5 out of 5 points

 

 

 

 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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