**MAT 540 WEEK 4 MIDTERM EXAM LATEST**

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**MAT 540 Week 4 Midterm Exam Latest**

**MAT540**

**MAT 540 Week 4 Midterm Exam Latest**

**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**

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

**Question 7**

Data cannot exhibit both trend and cyclical patterns.

**Question 8**

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

**Question 9**

__________ is a measure of dispersion of random variable values about the expected value.

**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**

Developing the cumulative probability distribution helps to determine

**Question 13**

A seed value is a(n)

**Question 14**

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

**Question 15**

Consider the following frequency of demand:

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

**Question 16**

__________ is absolute error as a percentage of demand.

**Question 17**

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 18**

__________ is a linear regression model relating demand to time.

**Question 19**

__________ is a category of statistical techniques that uses historical data to predict future behavior.

**Question 20**

Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

**Question 21**

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

**Question 22**

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

**Question 23**

__________ is the difference between the forecast and actual demand.

**Question 24**

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

**Question 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.

**Question 26**

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**

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**

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 ________.

**Question 29**

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 30**

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 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**

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 33**

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 34**

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

Year | Demand | Forecast |

2001 | 16 | 18 |

2002 | 20 | 19 |

2003 | 18 | 24 |

**Question 35**

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 ? = .2 and the smoothed forecast for July is 32. Determine the smoothed forecast for August.

**Question 36**

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 37**

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 38**

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 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.

**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 |

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.