Assignment 3
Due Date: October 18, 2010
QM 162/262 (100 marks)
Weight: 10%
Question 1 (20 Marks)
The following data (in the file TREASURY.xls) represent the three-month Treasury bill rates in the United States from 1991 to 2005. (The file treasury.xls is on the CD in the back of the text book).
Year
Rate
Year
Rate
1991
5.38
1999
4.64
1992
3.43
2000
5.82
1993
3.00
2001
3.40
1994
4.25
2002
1.61
1995
5.49
2003
1.01
1996
5.01
2004
2.17
1997
5.06
2005
3.89
1998
4.78
Source: Board of Governors of the Federal Reserve System,
federalreserve.gov
(a) Plot the data.
(b) Fit a three-year moving average to the data and plot the results.
(c) Using a smoothing coefficient of W = 0.40, exponentially smooth the series and plot the results.
(d) Repeat (c), using W = 0.15.
(e) Using results in (c) and (d), what is your exponentially smoothed forecast for 2006? Check the actual value for 2006.
(f) Compare the results of (c) and (d).
Question 2 (30 Marks)
The data in the file STRATEGIC.xls represent the amount of oil, in millions of barrels held in the U.S. strategic oil reserve, from 1981 through 2004. (The file strategic.xls is on the CD in the back of the text book).
Source: Energy Information Administration, U.S. Department of Energy, www.eia.doe.gov.
(a) Plot the data.
(b) Compute a linear trend forecasting equation and plot the trend line.
(c) Compute a quadratic trend forecasting equation and plot the results.
(d) Compute an exponential trend forecasting equation

(f) Using the most appropriate model, forecast the number of barrels, in millions, for 2005.
Question 3 (20 Marks)
The shellfish catch and the wholesale prices in a coastal city for 2000 and for 2008 are given in the following table (SHELLFISH.XLS).
Quantity (millions of kg)
Price per kg ($)
2000
2008
2000
2008
Clams
71
112
11.24
12.26
Crabs
335
301
11.09
12.28
Lobsters
30
30
11.73
12.63
Oysters
55
53
11.51
12.81
Scallops
23
13
11.65
12.69
Prawns
244
344
11.34
11.66
(a) By using 2000 as the base year, calculate the Paasche, Laspeyres and Fisher price indexes.
(b) Interpret the results.
Question 4 (15 Marks)
Handy Home Centre specialises in building materials for home improvements. They recently constructed an information booth in the centre of the store. Define X to be the number of customers who arrive at the booth over a 5-minute period. Assume that the conditions for a Poisson situation are satisfied with
λ=4 customers over a 5-minute period
(a) What is the probability that over any 5-minute interval, exactly four people arrive at the information booth?
(b) What is the probability that more than one person will arrive?
(c) What is the probability that exactly six people arrive over a 10-minute period?
Question 5 (15 Marks)
J.D. Power and Associates calculates and publishes various statistics concerning car quality. The initial quality score measures the number of problems per new car sold. For

2004 model cars, the Lexus had 0.78 problems per car. Assume that the number of problems per new car is distributed as a Poisson random variable. What is the probability that: {show your workings}
(a) a 2004 Lexus will have zero problems?
(b) a 2004 Lexus will have one or more problems?
(c) a 2004 Lexus will have two or less problems?
Marking policy
Plagiarism
You must comply with the University’s policy on Plagiarism and Academic Misconduct. The next section in this booklet directs you to the policy, outlines your responsibilities in connection with academic writing, and gives advice on how to avoid plagiarism.
Assessment preview
Asking unit coordinators for preliminary review of any assessment tasks prior to formal submission is inappropriate and unfair to other students without that opportunity.
Casual markers and moderation process
Students are advised that their assessment tasks may be marked by someone other than a member of the teaching team. If this is the case, the Head of School will approve the appointment of all casual markers, and the unit coordinator will moderate the marking process to ensure competence, fairness and consistency.
Extensions and late submission
If you find that you cannot meet the published due date for an assignment, you must contact the unit coordinator in writing no later than the due date to request an extension. Any required supporting information, such as a medical certificate, should be provided to the unit coordinator no later than the due date.
Extensions will be granted on the basis of unavoidable or unforeseen circumstances. However, requests that relate to avoidable time management issues such as ‘heavy work commitments in other units’ or ‘leaving my run a little late’ will not be considered favourably.
Except under exceptional circumstances, the maximum possible extension that may be requested is two weeks and only one extension is possible per assignment.
Assignments are deemed to be late if (i) they are not submitted (in accordance with the submission requirements outlined above) on, or before, the published due date or (ii)