Strayer MAT 540 Quantitative Methods Midterm Exam

• Question 1
 Deterministic techniques assume that no uncertainty exists in model parameters.    
 
•  Question 2
 A continuous random variable may assume only integer values within a given interval.    
 
•  Question 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.   
 
•  Question 4
 A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches.   
 
•  Question 5
 Excel can only be used to simulate systems that can be represented by continuous random variables.   
 
•  Question 6
 Starting conditions have no impact on the validity of a simulation model.   
 
•  Question 7
 Data cannot exhibit both trend and cyclical patterns.    
 
•  Question 8
 The Delphi develops a consensus forecast about what will occur in the future.   
 
•  Question 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?   
 
•  Question 10
 In Bayesian analysis, additional information is used to alter the __________ probability of the occurrence of an event.   
  
•  Question 11
 The __________ is the maximum amount a decision maker would pay for additional information.   
 
•  Question 12
 A seed value is a(n)   
 
•  Question 13
 Consider the following frequency of demand:

If the simulation begins with 0.8102, the simulated value for demand would be   
 
•  Question 14
 Random numbers generated by a __________ process instead of a __________ process are pseudorandom numbers.   
 
•  Question 15
 Developing the cumulative probability distribution helps to determine
 
•  Question 16
 __________ is absolute error as a percentage of demand.   
 
•  Question 17
 __________ is a category of statistical techniques that uses historical data to predict future behavior.   
 
•  Question 18
 In exponential smoothing, the closer alpha is to __________, the greater the reaction to the most recent demand.   
 
•  Question 19
 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:
If the forecast for period 5 is equal to 275, use exponential smoothing with α = .40 to compute a forecast for period 7.   
 
•  Question 20
 Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?   
  
•  Question 21
 Coefficient of determination is the percentage of the variation in the __________ variable that results from the __________ variable.   
 
•  Question 22
 Which of the following possible values of alpha would cause exponential smoothing to respond the most slowly to sudden changes in forecast errors?   
•  Question 23
 __________ is a linear regression model relating demand to time.   
   
•  Question 24 
 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 25
 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 26
 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 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.   
  
•  Question 28
 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 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.
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? Round your answer to the nearest dollar.

•  Question 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?   

•  Question 31
 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
 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.
 
•  Question 33
 Given the following data, compute the MAD for the forecast.
Year Demand Forecast
2001 16 18
2002 20 19
2003 18 24
     
•  Question 34  
 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  
 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.   
  
•  Question 36
 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 37
 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 38
 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.   
 
•  Question 39  
 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.   
 
•  Question 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.