INSTITUTE OF BANKERS IN MALAWI
DIPLOMA IN BANKING EXAMINATION
SUBJECT: INTRODUCTION TO BUSINESS STATISTICS (IOBM – D212)
Date: Thursday 3rd May 2012
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 multiple choice questions each carries 2 marks.
Answer ALL questions.
3
Section B consists of 4 questions, each question carries 20 marks. Answer ANY
TWO questions.
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.
6
Please write your examination number on each answer book used. Answer
sheets without examination numbers will not be marked.
7
DO NOT open this question paper until instructed to do so.
SECTION A
(60 MARKS)
Answer ALL questions in this section
Q1.
The sizes of the personal loans issued in 2011 to private customers of a banking
group can be modeled by a normal distribution with mean K4800 and standard
deviation K1200. The percentage of loans which are for amounts greater than
K3000 is:
A.
B.
C.
D.
Q2.
25.9%
84.1%
89.4%
93.3%
A bank found that 80% of their ATMs are in perfect working order. Five ATMs are
chosen at random and the bank wants to find the probability that all of them will
be in perfect working order. Choose the best answer of the following:
a.
b.
c.
d.
This is an example of a Poisson probability experiment
This is an example of a Binomial probability experiment
This is neither a Poisson nor a Binomial probability experiment
This is an example of a Normal probability experiment.
Q3.
The index that uses base year quantities as weights is called the
a.
Laspeyres index
b.
Paasche index
c.
Aggregate index
d.
Consumer price index.
Q4.
The number of customers that use a drive-in bank in a 5 minute period can be
modeled as a Poisson process. If on average 4 customers use the bank every
five minutes, what is the probability that most two customers will use the drive-in
bank in a 5 minute period.
a.
0.8
b.
0.25
c.
0.417
d.
0.238
A qualification examined by the Institute of Bankers in Malawi
2
Q5.
In testing for means, which test statistic is used when the sample size is small
and variance is unknown.
a.
Chi-squared statistic
b.
Normal z-statistic
c.
Students t-statistic
d.
F-statistic.
Q6.
The name of a discount rate which yields a net present value (NPV) of zero is
called:
a.
Accounting rate of return
b.
Internal rate of return
c.
Nominal rate
d.
Effective rate
Q7.
The mean age of managers for a certain bank is claimed to be 56.9 years. A
hypothesis test is performed at a level of significance of 0.01 with a p-value of
0.09. Choose the best interpretation of the hypothesis test.
a.
b.
c.
d.
Q8.
A researcher studying consumer buying habits questions every twentieth person
entering a supermarket. He asks, "How many times per week do you go grocery
shopping?" He then records the answer as T. Then [T = 3] is
a.
b.
c.
d.
Q9.
Reject the null hypothesis - there is enough evidence to reject the claim
that the mean age of managers is 56.9 years.
Reject the null hypothesis - there is enough evidence to support the claim
that the mean age of managers is 56.9 years.
Fail to reject the null hypothesis - there is no enough evidence to reject the
claim that the mean age of managers is 56.9 years.
Fail to reject the null hypothesis - there is no enough evidence to support
the claim that the mean age of managers is 56.9 years.
A sample space
A random variable
An event of interest
None of these.
If the size of the sample being used is increased, then the width of a 95%
confidence interval estimate for a population mean will
a.
b.
Become narrower
Become wider
A qualification examined by the Institute of Bankers in Malawi
3
c.
d.
Not be changed
The effect on the width cannot be determined from the given
information
Q10. All possible samples of size 10 were taken from a particular population. The
mean of all the sample means was found to be 12.7 and the variance of the
sample means was 0.32.
What are the mean and variance of the population?
a.
b.
c.
d.
12.7 and 3.2
12.7 and 0.032
12.7 and 1.27
12.7 and 10.32.
Q11. A bank claims that 45% of Malawians prefer its services. A sample of 200 people
includes 80 who prefer its services. To test if the claim is valid at 5% significance
level, the appropriate hypothesis would be.
a.
H 0 : p  0.45 and H 1 : p  0.45
b.
H 0 : p  0.45 and H 1 : p  0.45
c.
H 0 : p  0.45 and H 1 : p  0.45
d.
H 0 : p  0.4 and H 1 : p  0.4
Q12. The following are investment appraisal techniques except:
a.
b.
c.
d.
Payback period method
Net present value
Accounting rate of return
Depreciation rate method
Q13. An index number increases by 7% each year of its value in the previous year. If
its value in 2007 was 160, its value in 2012 is closest to
a.
b.
c.
d.
195
196
197
198.
Q14. Based on the last fifteen periods, the underlying trend of sales is:
y  345.12  1.35 x
A qualification examined by the Institute of Bankers in Malawi
4
If the sixteenth period has a seasonal factor of  23.62 , assuming an additive
forecasting model, then the forecast for that period, in whole units, is:
a.
b.
c.
d.
300
343
347
390.
Q15. A bank’s profits have been as follows (Km):
Year
2007
Profits 410
2008
370
2009
350
2010
380
2011
390
When converted to index numbers with base 2007, the index for 2011 is
a.
95
b.
105
c.
- 0.2
d.
5
Q16. A company charges depreciation at the rate of 25% per annum on the reducing
balance method on an asset that cost K200,000. At the end of year three the
written-down value will be
a.
K50,000
b.
K115,605
c.
K105,000
d.
K84,375
Q17. The trend of a time series can be estimated using the following methods except
a. moving averages
b. least squares regression
c. semi-averages method
d. the method of undetermined coefficients
Q18. A project may result in profits of K20m or K12m, or in a loss of K5m, with
probabilities 0.3, 0.5 and 0.2, respectively. What is the expected profit?
a.
K11m
b.
K27m
c.
K9m
d.
K12m
Q19. If weights of bank parcels are normally distributed with mean 65 g and standard
deviation 8 g, what is the probability of a weight being less than 7 kg.
a.
0.2357
b.
0.7357
c.
0.7643
d.
0.2643
A qualification examined by the Institute of Bankers in Malawi
5
Q20. A random sample of 100 invoices yielded a mean gross value of K45,500 and
standard deviation K3,240. What is the 95% confidence interval for the
population mean?
a.
[43,285, 47,850]
b.
[30,320, 48,250]
c.
[44,865, 46,135]
d.
[40,200, 50,640]
Q21. A bank is investigating customer preference of its customers. The table below
contains information relating to the age of customer and the type of account they
prefer. The data was collected from a random sample of 400 regular customers.
Account Type
Savings
Current
Under 25
20
60
Age of customers (years)
25 – 39
40 – 59
60 and over
25
70
40
95
80
10
The bank wishes to test if there is any association between account
preferred and the age of a customer. Which test statistic would you use?
a.
b.
c.
d.
type
Chi-squared statistic
Normal z-statistic
Students t-statistic
F-statistic
Q22. In reference to the information as presented in Q21, how many degrees of
freedom would be used?
a.
4
b.
2
c.
1
d.
3.
Q23. A company produces three products X, Y and Z. Unit costs for products X, Y and
Z are K230, K350 and K200 respectively. It takes 2 hours to make one unit of X,
1 hour and 3 hour to make one unit of product Y and Z respectively. If there is a
maximum of 150 labour hours available besides other constraints and the
company plans to make x , y and z units of products X, Y and Z respectively,
then the appropriate inequality is
a.
b.
c.
d.
230 x  350 y  200 z  150
230 x  350 y  200 z  150
2 x  y  3z  150
2 x  y  3z  150
A qualification examined by the Institute of Bankers in Malawi
6
Q24. What is the present value of K15,000 in 3 years at a discount rate of 15% per
annum.
a.
K12,381
b.
K9,863
c.
K22,813
d.
K11,218.
Q25. An index number is made up of two items, A and B, as follows:
Subgroup
A
B
All
Weight
7
3
10
Index
130
X
127
The number for subgroup B (X) is closest to
a.
120
b.
123
c.
125
d.
128
Q26. From past records, 2% of auto-teller machines break down during peak times. If
there are 8 auto-teller machines in a busy shopping area, what is the probability
that exactly two of them will break down during peak time?
a.
0.9921
b.
0.8858
c.
0.0099
d.
0.0004
Q27. A bank credit card department claims that 60% of all card holders do not pay
their bills on time. In a random sample of 200 cardholders, 136 are behind in their
bills. The bank wishes to test if the claim is low at 1% level of significance.
The value of the normal z test statistic is
a.
2.309
b.
– 2.309
c.
2.58
d.
- 2.58
Q28. For any two random variables A and B, which of the following statements must
be true?
II.
 A B   A   B
 A B   A   B
III.
 A2  B   A2   B2
I.
a.
I only
A qualification examined by the Institute of Bankers in Malawi
7
b.
c.
d.
II only
II and III
I and II
Q29. An opinion survey will be conducted at three corporations. Corporation A has
4,000 employees, corporation B has 6,000 employees and corporation C has
15,000 employees. The results of each survey will be used to estimate the
opinions of employees at each corporation. Each survey will be conducted with a
simple random sample of 500 employees. Which corporation will have its
employees opinions estimated more accurately by the surveys?
a.
b.
c.
d.
Corporation B
Neither corporation will have a more accurate estimate
Corporation C
Corporation A
Q30. The distribution of a bank’s customers at Chuma service centre is as follows:
Sex
Male
Female
Current account
290
30
Savings account
660
1020
A customer’s account is chosen at random. If the account chosen belongs to a
female customer, what is the probability that she has a savings account?
a.
b.
c.
d.
0.510
0.525
0.607
0.840
A qualification examined by the Institute of Bankers in Malawi
8
SECTION B (40 MARKS)
Answer any TWO questions from this section
QUESTION 1
a)
Cite any one use of the normal distribution.
b)
A bank’s records show that the weekly distance travelled by their salesmen is
approximately normally distributed with mean 1280 km and standard deviation
144 km. Their manager considers that salesmen who travel less than 960 km in
one week are performing poorly.
c)
(1 marks)
(i)
If the bank employs 200 salesmen, how many would be expected to
perform in a particular week.
(7 marks)
(ii)
The manager wishes to identify the distance travelled in one week above
which 1% of salesmen are expected to exceed. What weekly distance is
this.
(5 marks)
The customer care department of a bank keeps records of complaints made by
its clients over the course of a week. The data are given in the following table.
Day
Mon
Number of 12
Tue
Wed
Thur
Fri
Sat
15
8
14
23
28
complaints
At   0.01 level of significance, is there any difference in the number of complaints
made based on the day of the week?
(7 marks)
(Total 20 marks)
A qualification examined by the Institute of Bankers in Malawi
9
QUESTION 2
(a)
(i)
Briefly explain why interest is paid.
(2 marks)
(iii)
What is the Internal Rate of Return and state what it indicates?
(2 marks)
(b)
The following data give the quantities and costs of materials for the four
service centres for a local bank for two years.
Cost (K’000)
Service
Quantity (tones)
Centre
2010
2011
2010
2011
A
175
201
1540
1830
B
32
46
1270
1490
C
48
43
2760
2490
D
65
66
2190
2070
Using 2010 as the base year, calculate:
(i)
The Paasche cost index
(4 marks)
(ii)
The Laspeyres quantity index.
(4 marks)
(c)
A firm is considering buying a machine costing K200,000 and the
expected net cash flows are as follows;
Year
1
2
3
4
5
Net cashflow (K)
50,000
55,000
65,000
75,000
75,000
Assuming the cost of capital is 10%, should the firm buy the machine? Use Internal
Rate of Return (IRR) method and another rate of interest of 15%.
(8 marks)
(Total 20 marks)
A qualification examined by the Institute of Bankers in Malawi
10
QUESTION 3
(a)
A set of customer accounts is known to have errors in about 3% of them.
An auditor’s operational scheme for a set of accounts of this size
sample 12 of them randomly and, if no errors are found, to
is
pass
to
the
accounts as acceptable. If any error is found in the sample, all accounts
are then inspected. The auditor always finds any errors in accounts that
are checked.
(i)
Describe the probability distribution of the number of errors.
(2 marks)
(ii)
What is the probability that all the errors in the accounts will be
detected?
(iii)
(4 marks)
What is the minimum sample size necessary to ensure that the
auditor has a better than even chance of discovering all the errors
in the accounts?
(b)
(6 marks)
Describe any two methods of investment appraisal and for each method
give one advantage and one disadvantage.
(8 marks)
(Total 20 marks)
QUESTION 4
(a)
Briefly describe the components that make up a time series and for
each give an illustrative example.
(b)
Suggest any two areas or situations in which you would apply quality
control in the banking sector.
(c)
(8 marks)
(2 marks)
A bank has investigated customers’ complaints. The following table
summarises the replies received.
A qualification examined by the Institute of Bankers in Malawi
11
Type of complaint
Number of complaints
Poor lighting
350
Unfriendly personnel
1100
Small banking hall
420
Noisy surrounding
167
No air-conditioning
82
Poor service
972
Lack of washrooms
745
Small parking space
189
(i)
Draw a Pareto chart.
(6 marks)
(ii)
Comment on your findings.
(4 marks)
(Total 20 marks)
END OF EXAMINATION PAPER
A qualification examined by the Institute of Bankers in Malawi
12