1
ISOM111 Business Statistics
Final Examination
For section L5 only
15 December 2008
Directions
1)
Answer
ALL FIVE
questions. Marks are shown in square brackets.
2)
There are 4 pages in this examination paper including the cover page. Check to
make sure you have a complete set and notify the invigilator immediately if
part of it is missing.
3)
Key formulas and Statistical tables are provided separately.
4)
Calculator may be used in this examination.
5)
You are given THREE HOURS to complete this examination. Do not begin
until you are told to do so.

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Question 1:
[16 Marks]
An investment management firm engages in trading risky assets such as stocks and options
daily. Let the random variable
X
denote the daily profit-and-loss (P&L); a positive value of
X
indicates a profit and negative value a loss. Assume
X
has mean $10,000 and standard
deviation $40,000. We assume that outcomes from day to day are independent.
(a)
Let’s say there are five working days in a week. What is the mean and standard deviation
for the total P&L in a week?
(b)
Consider the average of P&L in a week. What is the standard error for weekly average?
(c)
What is the probability that the company will suffer a loss in 50 days? Do you need to
make any assumption on the probability distribution of
X
to answer this question? Please
explain briefly.
(d)
Please provide the necessary assumption on the distribution of
X
and calculate the
probability that the company will lose more than $40000 in 10 days.
Q
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2
:
[
2
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M
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]
A company sells women’s clothing and accessories by direct mail. Two types of catalogues were
sent to different groups of customers. Catalogue A generated orders from 30 customers in a
group of 1000 customers and Catalogue B received orders from 50 customers in another group
of 1000 customers.
(a)
Please test the null hypothesis at 5% significance level that the response rates are the
same for the two types of catalogues.
(b)

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