BEA140 Quantitative Methods Assignment 3
Students should ensure that they have read and understood the guidelines for the assignment (attached)
Question 1
Kim, Lee and Bob are three telephone consultants who work for an insurance company, answering phone calls and
provding car insurance quotes. Their call durations are as follows:
Kim: call duration follows a normal distribution with mean 550 seconds and standard deviation 160 seconds.
Lee: call duration follows a normal distribution with mean 550 seconds and standard deviation 75 seconds.
Bob: call duration follows a normal distribution with mean 600 seconds and standard deviation 75 seconds.
Management consider call durations between 500 seconds and 700 are of acceptable duration. (They believe that if
a call is shorted than 500 seconds the consultant will not have had enough time to gather all the required
information, and any call longer than 700 is wasting time.) Bob takes 25% of the call volume, Lee takes 35% and Kim
takes the rest.
a) Determine the probability that a call is of acceptable duration given it was
Answered by Kim
Answered by Lee
Answered by Bob.
[3+3+3 = 9 marks]
b) Present the various combinations of call answering events (Kim / Lee / Bob, and acceptable / not
acceptable) in a fully labelled tree diagram, showing marginal, conditional and joint probabilities.
[8 marks]
c) Determine the probability that a randomly selected call is NOT acceptable
[2 marks]
d) If a randomly selected call is NOT acceptable, determine the probability it was taken by:
Kim
Lee
Bob.
If the level of acceptable performance could be improved through training, and you only had enough
budget to train one consultant, explain which consultant you would choose.
Assumptions identified but misstated assumption required to allow the use
1 NB Sometimes questions may not need students to state any assumption as these may have been provided in the question.
2 If a student makes a mistake on a question part they will lose marks on that question part. If they then use a resulting inco rrect number in a subsequent
question part, as far as possible they will not penalised in that subsequent part, except where it should have become obvious to the student that an error was
carried in.
3 For instance, if a diagram is required as part of an answer to part (b), it should be with the rest of part (b) and between parts (a) and (c). If a diagram is too
large to fit into the answer sequence it should be included as an appendix at the end of the document, with a clear reference to it in the answer sequence. E.g.
“see appendix 3 for the diagram associated with the answer”.
Guidelines for BEA140 Quantitative Methods Assignment
Teams Individuals
The assignment may only be completed and submitted by individuals. Team assignments are not allowed.
Whereas students are encouraged to discuss all elements of the unit, including the assignment, the preparation of the
assignment must be an individual effort. For example, two or more students discussing how to attack question 2, for example,
is acceptable. Two students working together to prepare a full solution to question 2 is NOT acceptable. A student presenti ng
others’ work as their own is NOT acceptable. A student allowing another student to copy all or part of their assignment is NOT
acceptable. (See note about plagiarism at bottom of page.)
Presentation
Assignments must be submitted with a completed cover sheet. If an assignment is submitted without, the assignment and
mark will be withheld until the student submits it.
The assignment should be prepared on a word processor, and submitted as a “.docx”, “.pdf”, “.doc” or “.rtf” document. It is
imperative that students carefully read the Assessment Guidelines Rubric (previous page). Students are expected to show
sufficient working such that the marker can establish the logic of their thoughts . (Typically, the amount of working in examples
in the lectures is a good indication of what is an acceptable amount of detail.). Part marks will be available for incorrect
answers, and will be allocated on the basis of the working.
Preparation Methodology
Students are encouraged to check their answers, and ask themselves questions such as "DOES THIS MAKE SENSE?", "HOW CAN I
TELL IF THIS LOOKS REASONABLE?" If a student gets an answ er that is obviously w rong and can't figure out w hat has gone w rong, they
are expected to at least comment that it does not look reasonable (and w hy).
Students are encouraged to complete assignment questions as the relevant topics are covered in class . (The "MAD RUSH AT THE
LAST MINUTE" strategy is a dangerous one. See PROBLEMS below.)
Problems
Assignments that are handed in late will be penalised, unless prior arrangement has been made with the lecturer. Assignments
up to one week late will be penalised as described in the unit outline. Assignments more than one week late will not be
marked.
In the event of sickness or other major disruption is likely to affect a student’s ability to submit the assignment on time, the
lecturer should be contacted a.s.a.p. Special consideration will require documentary evidence. (Medical certificate, memo
on letterhead for participation in representative (Tas, or Aust) sport or for interstate work commitments, etc0)
Special consideration will most likely assume that the individual was working on the assignment as recommended in the
Preparation Methodology section above. For example, if one is sick for the last week before the assignment is due, it may well
be expected that all of the assignment that should have been prepared during previous weeks will be submitted on time, and
that only the questions pertaining to the last week's work will be granted an extension.
If you have any other questions or problems contact your lecturer or workshop tutor - the earlier the better.
Marking and Feedback
It will take a number of weeks to mark the assignment.
However, one week after the due date, a full and detailed set of solutions will be posted on mylo. Students are encouraged to
keep a copy of their assignment which they can check against the solutions, and thus obtain feedback on their performance
even before the assignments are marked. This strategy is designed to allow students to take maximum advantage of the
assignment in their exam preparation study.
Upon return of marked assignments, teaching staff will be available for those students seeking more feedback.
You should be aware that assignments will be checked for plagiarism. Plagiarism is punishable by reduction or cancellation of
marks, and in the most serious cases, exclusion from a unit, a course or the University. This applies both to a student who s ubmits
somebody else’s work as their own, AND to a student who willingly allows another to copy and submit their work.