# Consumer Behaviour by qKQ55N

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```									             INSTITUTE OF BANKERS IN MALAWI

CERTIFICATE IN BANKING EXAMINATION

SUBJECT: FUNDAMENTALS OF BUSINESS STATISTICS (IOBM – C103)

Date: Monday, 31st October 2011

Time Allocated: 3 hours (08:00 – 11:00 am)

INSTRUCTIONS TO CANDIDATES
1     This paper consists of TWO Sections, A and B.
2     Section A consists of 4 questions, each question carries 15 marks.
3     Section B consists of 4 questions, each question carries 20 marks.
4     You will be allowed 10 minutes to go through the paper before the start of
the examination, you may write on this paper but not in the answer book.
5     Begin each answer on a new page.
Answer books without examination number will not be marked.
7     DO NOT open this question paper until instructed to do so.

A qualification examined by the Institute of Bankers in Malawi             Page 1
SECTION A                                        (60 MARKS)

Answer ALL questions from this section.

QUESTION 1

The following chart shows the number of customers visiting a bank per hour over
a period of 1000 hours.

Number of customers visiting a bank
40
35
Percentage frequency

30
25
20
15
10
5
0
0       1       3        5      8         12   16    20
Number of customers

a)    What is the chart called?                                                                 (1 mark)

b)    Identify one major mistake in the construction of the chart and reconstruct
the chart with the mistake corrected.                             (3 marks)

c)    In how many hours did the bank receive 2 up to 4 customers?                              (2 marks)

d)    Construct a frequency distribution clearly showing the class boundaries,
frequencies, and cumulative more-than frequencies.             (5 marks)

e)    Find the mean of the distribution.                                                       (4 marks)

(Total15 marks)

A qualification examined by the Institute of Bankers in Malawi                                   Page 2
QUESTION 2

a)         Explain the difference between:

i.     a population and a sample                                       (3 marks)
ii.     mutually exclusive and exhaustive events                        (4 marks)

b)         List the four levels of measurement and give an illustrative example of
each level.                                                   (8 marks)

(Total 15 marks)

QUESTION 3

The following set of data represents the annual payouts (K’ million) made by
Malawian insurance companies in 2010:

Payout (K’ million)                 Frequency
less than 20                       10
20 and less than 40                    35
40 and less than 60                    40
60 and less than 80                    10
80 and less than 100                    3
100 and less than 120                    2

a)         Calculate the standard deviation of the distribution.             (5 marks)

b)         Find the median of the distribution using the formula.            (5 marks)

c)     In how many instances did the companies payout in excess of K40,
000,000?                                                (2 marks)

d)         Find the coefficient of skewness of the distribution using the formular.
(3 marks)

(Total 15 marks)

A qualification examined by the Institute of Bankers in Malawi                  Page 3
QUESTION 4

a)          The following shows the distribution of the difference between “actual” and
“ideal” account balances for 119 student customers of a local bank. Ideal
balances were responses to the questionnaire item ‘What is your ideal
account balance?’ Note that the “difference” is “actual balance” minus
“ideal balance”.

35
30
25
Percent (%)

20
15
10
5
0
-20 -15 -10 -5   0   5   10   15   20   25    30   35   40   45   50   55
Difference = Actual - Ideal

i.                  What name is given to this chart?                                           (2 marks)

ii.                  What is the approximate direction of skewness of the distribution?

iii.                 Approximate the mode of the distribution graphically.                       (3 marks)

b)          Two components X and Y have probabilities of 0.75 and 0.875
respectively of functioning. They function independently of one another. A
device is constructed using the two components and it works whenever at
least one of the components is functioning.

i.                  Find the probability that the device works.                                 (3 marks)

c)          Give two reasons why non-response is a problem in statistical surveys.
(4 marks)

(Total 15 marks)

A qualification examined by the Institute of Bankers in Malawi                                             Page 4
SECTION B

Answer ANY TWO question from this section

QUESTION 5

a)    The charge for parking at “Katoto Car Park” depends on how long a car is
parked rounded to the next hour. Penalties are imposed on cars parked for
a period of over 6 hours. The parking times for a random sample of 60
cars were recorded to the nearest minute. A stem-and-leaf display of the
times is shown below:

Parking times in minutes

Hundreds     Tens
0     1124
0     5555556
1     0123344
1     5566667777799
2     022233334
2     556799
3     00123
3     5555666
4
4     9
5     2

i.    Explain clearly what the entries in the display signify. By referring to
the entry 4|9, identify the “stem” and the “leaf”.            (3 marks)

ii.   Comment on the distribution of the times. What does this distribution
suggest about the charging policy at Katoto Car Park?     (3 marks)

iii. Suppose each of the times recorded had units digit of 5, find the
median, lower quartile and upper quartile of the distribution of the
parking times.                                             (5 marks)

b)    As part of expansion drive a bank collected the following data on the
population of a small rural trading centre:

A qualification examined by the Institute of Bankers in Malawi              Page 5
Age (years)           Number of persons
Below 5                      39
5 but below 15                   92
15 but below 30                 122
30 but below 45                  99
45 but below 65                 130
65 but below 75                  50
75 but below 105                  28

i.    Find the probability that a randomly selected person is at least 45
years old.                                                (3 marks)

ii.   What type of probability is applied in (i) above?                    (1 mark)

iii. Find the median age of the population.                              (5 marks)
(Total 20 marks)

QUESTION 6

A manager of a local bank was interested in the relationship between the number
of personal loan applications and the prevailing interest rates. She took a random
sample of 8 months from January 2008 to October 2011:

Month           1        2       3       4        5         6         7        8
Interest rate     14.0     13.7    14.5    13.5     12.0      12.3      14.8     13.3
(%)
№ of loan           27       40      24      32       64       52         21      43
applications

a)    Represent the data on a scatter diagram. Use a scale of 1:0.5 on the x-
axis and 1:5 on the y-axis.                                   (4 marks)

b)    Determine the least squares linear regression equation for predicting the
number of loan applications given interest rate.
(7 marks)
c)    Plot the least squares regression equation on your scatter diagram. Which
month was the best compared to predicted number of loan applications?
(3 marks)

A qualification examined by the Institute of Bankers in Malawi                    Page 6
d)              Find the correlation coefficient between interest rate and number of loan
applications. Comment on its value.                            (4 marks)

e)              What percentage of variations in the number of loan applications is
explained by variations in the interest rate?             (2 marks)
(Total 20 marks)

QUESTION 7

a)              Distinguish carefully between a pilot survey, a sample survey and a
census, giving reasons why each might be conducted.        (9 marks)

b)              Give four possible reasons why results from a census would differ from
the true values in the population                          (4 marks)

c)              The Institute of Bankers in Malawi is interested in finding details relating to
the occupations of its graduates two, five and ten years after completing
their studies with the institute. The institute considers e-survey as their
major survey method.

i.        Explain what you understand by e-survey.                         (1 mark)

ii.       Briefly explain two reasons why e-surveys are becoming popular
these days.                                          (4 marks)

iii.          What major drawback is the institute likely to face in the
implementation of the e-survey?                     (2 marks)
(Total 20 marks)

QUESTION 8

a)           What is meant by saying two events A and B are independent in terms
of:
i.               .                                                (2 marks)

ii.               .                                                       (2 marks)

A qualification examined by the Institute of Bankers in Malawi                         Page 7
b) A committee of 5 is to be chosen from 4 men and 5 women to work on the
launch of a new bank product. What is the probability that the committee
will include at least 4 women?                                  (5 marks)

c)      A bank has two major service portfolios, retail and corporate. A financial
analyst predicts that the corporate portfolio has a probability of 0.7 of
showing profit at the end of the year. She further estimates that the retail
portfolio has only a 0.5 probability of giving a profit, but if it does so, she
argues that the corporate portfolio would have a 0.9 probability of also
being profitable.

i.    Find the probability that both will be profitable.              (4 marks)

ii.   What is the probability that at least one will be profitable?   (3 marks)

iii.   Are the two portfolios independent in terms of being profitable?
(4 marks)

(Total 20 marks)

END OF THE EXAMINATION PAPER

A qualification examined by the Institute of Bankers in Malawi                  Page 8

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