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QUANTITATIVE
METHODS FOR MANAGERS
Instructions to candidates:
a) Time
allowed: Three hours (plus an extra ten minutes’ reading time at the start – do
not write anything during this time)
b)
Answer any FIVE questions
c) All
questions carry equal marks. Marks for each question are shown in [ ]
d)
Non-programmable calculators are permitted in this examination
1. a) Use a simple example
to demonstrate the meaning of spurious correlation .
[5]
b) The
personnel department of a large marketing organisation holds regular interview
days where potential candidates are required to undergo an interview and a numeracy
test. The results for one particular session are shown in the following table:
Candidate
A
B
C
D
E
F
G
H
Interview rank
5
1
3
2
6
8
7
4
Numeracy test score
70
85
80
75
60
60
58
83
Calculate the Rank
Correlation Coefficient, and use this to comment on the level of agreement
between the interview
and testing process
.
2. A
large builders’ merchant has estimated that the number of days between sending
out a monthly invoice and receiving the payment from its customers is normally
distributed with a mean of 16 days and a standard deviation of 4 days.
a) Find
the probability that an invoice will not be paid until after 18 days. [5]
b) From
200 invoices, how many would be expected to be paid between 12 days and 22
days? [8]
c) As
an incentive to pay early, the company offers to reward the quickest 10% of
customers with a
5%
discount on their bills. On what day should the incentive be set? [7]
3. The
customer helpline of an insurance company operates from Monday to Friday. As
part of a quality assurance exercise, the company monitors the calls to the
helpline over a period of three weeks, and the following table shows the
results of this exercise:
Week
1
2
3
Day
M
Tu
W
Th
F
M
Tu
W
Th
F
M
Tu
W
Th
F
No. of enquiries
33
41
77
81
99
39
49
84
90
107
47
55
91
102
113
a) Plot a graph of the
above time series, and comment on any movements that are present.
[4]
b)
Using the above graph, decide what will be the most appropriate moving average,
and use this to superimpose the trend line on your graph. [8]
c)
Calculate the seasonal component for Monday. [5]
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