INSTITUTE OF BANKERS IN MALAWI
DIPLOMA IN BANKING EXAMINATION
SUBJECT: INTRODUCTION OF BUSINESS STATISTICS
(IOBM – D212)
Date: Wednesday, 1st May 2013
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 20 multiple choice questions, each question carries 2
marks.
Answer ALL questions.
3
Section B consists of 5 questions, each question carries 20 marks. Answer ANY
THREE questions.
4
You will be allowed 10 minutes to go through the paper before the start of the
examination, when 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
books without examination numbers will not be marked.
7
You are provided with the following to assist you in the examinations:
(i)
(ii)
(iii)
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Graph sheet.
Chi square and Normal Distribution tables.
Formulas.
DO NOT open this question paper until instructed to do so.
SECTION A
(60 MARKS)
Answer ALL questions from this section
1. A chi-squared test involves a set of counts called ‘expected frequencies’.
Expected frequencies are:
a.
b.
c.
d.
hypothetical counts that would occur if the alternative hypothesis were true
hypothetical counts that would occur if the null hypothesis were true
actual counts that occurred in a data set
theoretical counts that would occur if the degrees of freedom were increased.
2. The probabilities that a bank receives 2, 3, 5 or 7 overdraft applications
on
any given day are 0.35, 0.41, 0.15 and 0.09 respectively. Calculate the expected
number of overdraft applications on any given day.
(a) 4.25
(b) 3.52
c.
d.
3.25
3.31
3. What is the future value of K5,000 invested for 8 years at 12% compounded
annually?
a. K15,813.68
b. K12,379.82
c.
d.
K9812.82
K13,279.92
4. In a chi-squared goodness-of-fit test with 10 categories, the critical value at
0.05 significance level is
a. 16.919
b. 18.307
c.
d.
15.987
14.684
5. A feasible solution to a linear programming problem
a.
b.
c.
d.
must satisfy all the problem’s constraints simultaneously
need not satisfy all of the problem constraints, only some of them
must be a corner point of the feasible region.
must give the maximum profit
6. One of the following is NOT a condition for the Binomial probability distribution
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a.
b.
c.
d.
there are two possible outcomes called success and failure
there are n independent trials
the probability of success is constant at each and every trial
events occur in space or interval of time
7. Using the table of areas under the standard normal curve, find P 1  z  2
where z ~ N 0,1
a.
b.
0.8185
0.3413
c.
d.
0.4772
0.0618
8. Given that n  50 , x  30.2 and   5.1. Find the 95% confidence for the true
population mean.
a.
b.
[28.2, 30.5]
[29.3, 32.0]
c.
d.
[25.3, 34.2]
[27.7, 32.0]
For questions 9 – 10:
In a survey, customers were asked to indicate their preferred bank. The results are
summarized below:
Preferred Bank
Khusa
Number
customers
118
Pamwamba
Wotsogola
Tilipo
95
102
135
of
9. To test the claim that preference for the bank is uniform, the null hypothesis
would be stated as follows:
a.
b.
c.
d.
the level of preference for the bank is the same for each service station
more customers prefer Tilipo bank
the level of preference is not the same among the banks
there is a difference between observed and expected sets of frequencies.
10. The expected frequencies for the bank are:
a. 118; 95; 102; 135
b. 112.5 each
c.
d.
450 each
150 each
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11. Which one of the following is NOT a time series component?
a. control factors
b. trend
c.
d.
cyclic variation
seasonal variation
12. An event A will occur with probability 0.5. An event B will occur with probability
0.6. The probability that both A and B will occur is 0.1. The conditional
probability of A given B is
a.
b.
c.
d.
Cannot be determined from the information given
0.167
0.200
0.833.
13. For the 90% confidence interval the critical z-value is
a.
b.
c.
d.
1.965
2.584
1.645
2.645
14. The index that measures the change from month to month in the cost of a
representative ‘basket’ of goods and services of the type bought by a typical
household is called
a.
b.
c.
d.
Paasche Price Index
Financial times Index
Retail Price Index
Laspeyres Price Index
15. Which of the following methods of Investment appraisal allows for the effects of
inflation on the real value of net cash flows?
a.
b.
c.
d.
Payback
Net Present Value
Accounting Rate of Return
None of the above.
16. The probability distribution of a random variable X is given in the following table.
X
P(X=x)
1
0.10
2
0.16
3
0.11
4
0.16
5
0.14
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0.33
4
Find the mean of the given probability distribution.
a. 4.07
c.
0.17
b. 3.50
d.
3.94
17. Consider a linear programming problem with the objective function
Maximize Z  50 x  80 y
The following points x, y  lie on the vertices of the feasible region:
0,0 , 28,0 , 20,6 , 8,12 and 0,12
The maximum possible profit for the objective function is
a. 1360
b. 1480
c.
d.
1400
960
18. Given that, for the events A and B: n  A  25 , n B   15 and n  A  B  10 ,
calculate P A | B.
a. 0.37
b. 0.47
c.
d.
0.57
0.67
19. The wholesale price index in Zaone shop is made up of the prices of three items.
The prices of each item and weighting in 2009 and 2012 are as follows.
Item
Margarine
Cooking oil
Sugar
2009 price (K)
200
1000
200
2012 price (K)
400
1200
250
Weight
60
20
40
Calculate the weighted price index of the shop for 2012.
a. 1.62
b. 1.89
c.
d.
1.52
1.98
20. The following probability distribution is used when the sample size is small and
the standard deviation is unknown;
a.
b.
c.
d.
Normal distribution
t-distribution
exponential distribution
chi-squared distribution
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SECTION B
(60 MARKS)
Answer ANY THREE questions from this section
QUESTION 2
(a)
(i)
Define the term ‘payback period’.
(1 mark)
(ii) Cite one advantage and one disadvantage of payback period as a method of
investment appraisal.
(2 marks)
(iii) Muswela Enterprise is planning to undertake another project requiring initial
investment of K50 million and is expected to generate the following returns:
Year
1
2
3
4
5
Returns
10
13
16
19
22
(K million)
Required:
Find the payback period for the project.
(b)
(4 marks)
(i) Briefly explain the significance of the Central Limit Theorem in statistical
inference.
(2 marks)
(ii) A large bank wishes to estimate the average number of pages typed by the
secretaries in a typing pool. A random sample of 50 secretaries is chosen
and their average production is 32 pages with a standard deviation of 6
pages.
Required:
Find the 96% confidence interval for the mean production of all secretaries
and how wide is the interval?
(5 marks)
(c)
A study of loan defaulters has shown that 2 in 10 customers default.
Find the probability that:
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(i)
(ii)
Exactly 2 of 8 customers are likely to default on loan repayment.
(3 marks)
At least 2 of 8 customers are likely to default on loan repayment.
(3 marks)
(Total 20 marks)
QUESTION 3
(a)
(i)
Cite any two properties of the normal probability distribution.
(ii)
(2 marks)
A bank records that customers’ monthly overdrafts are normally distributed
with mean K36,000 and standard deviation K10,000. The bank has 5,000
customers.
Find :
i. The number of customers with overdrafts of over K40,000.
ii. The percentage of customers with overdrafts of less than K41.000
(5 marks)
(3 marks)
iii. The number of customers with overdrafts between K30,000 and K40,000.
(5 marks)
(b)
A bank must make a choice between two projects, A and B. The following table
shows the probability distributions of possible profits from the two projects:
Project A
Probability
Profit (MK million)
0.4
35
0.5
60
0.3
40
0.1
25
Which project would you choose and why?
Project B
Probability
Profit (MK million)
0.2
20
0.3
25
0.3
40
0.1
80
0.1
120
(5 marks)
(Total 20 marks)
QUESTION 4
(a)
(i) Define ‘objective function’ within the context of linear programming.
(2 marks)
(ii) One method for solving linear programming models is the graphical method.
Briefly describe the steps involved in solving a linear programming problem
once a model has been formulated.
(4 marks)
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(iii) An oil refinery uses Tiyesenawo Bank as its agent bank for settling payments
for its foreign oil suppliers. As part of the agreement the bank is interested to
know quantities of the refined product.
The oil refinery can buy light crude at K31500 per barrel and heavy crude at
K27000 per barrel. Refining one barrel of oil produces petrol, heating oil, and
jet fuel as follows:
Oil grade
Petrol
Light
crude 0.3
Heavy crude
0.3
Heating oil
0.2
0.4
Jet fuel
0.3
0.2
The refinery has contracts for 0.9 million barrels of petrol, 0.8 million barrels of
heating oil and 0.5 million barrels of jet fuel.
Required:
How much light and heavy crude should the refinery buy to satisfy the contracts
at least cost?
(8 marks)
(b)
An insurance company divides its policy holders into three categories: low risk,
moderate risk, and high risk. The low-risk policy holders account for 60% of the
total number of people insured by the company. The moderate-risk policy holders
account for 30%, and the high-risk policy holders account for 10%. The
probabilities that a low-risk, moderate-risk, and high-risk policy holder will file a
claim within a given year are respectively 0.01, 0.10 and 0.50.
Required:
Given that a policy holder files a claim this year, what is the probability that the
person is a high-risk policy holder?
(6 marks)
(Total 20 marks)
QUESTION 5
(a)
Cite any two situations in which Poisson random variable occur.
(2 marks)
(b)
On a busy day, a bank’s customer care desk handles, on average, five queries
every 3 minutes. What is the probability that, on any busy day, there will be:
(i)
No queries?
(3 marks)
(ii)
At least two queries?
(4 marks)
(iii)
Exactly three queries if it turned out that the customer care desk was now
handling 30 queries every 45 minutes?
A qualification examined by the Institute of Bankers in Malawi
(3 marks)
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(c)
A survey is conducted among customers of a bank to determine if there is any
association between choice of bank account and their level of education. The
results of the survey are as follows:
Education
Level
Primary
Secondary
Graduate
Savings
100
300
20
Account Type
Current
Investment
200
50
400
80
30
5
Fixed
30
70
5
At 5% level of significance, test if there is any association between choice of bank
account and their level of education.
(8 marks)
(Total 20 marks)
QUESTION 6
(a)
(b)
A farmer invests K75,000 with a bank. The money will earn 12% interest
compounded annually. How long will it take for the money to double?
(5 marks)
(i)
Explain briefly what the consumer price index measures.
(1 mark)
(ii)
In 2012 a typical Malawian urban family ate 10 kgs of chicken and 8 kgs of
beef when the price of chicken was K500 per kg while the price of beef
was K800 per kg. In 2010, the price of chicken was K400 per kg while the
Price of bee was K500 per Kg.
Required:
Using the 2010 as the base year, calculate the Consumer Price Index for 2012
and interpret the result obtained. Assume that the basket for 2012 is given the
value of K5000.
(8 marks)
(c)
A financial analyst claims that the average number of cheques that are
referred to drawer at Nanchibwe Bank is 36. A random sample of 64
service centres shows a mean size of 37 cheques with a standard deviation of 6
cheques referred to drawer.
Test at 5% level of significance if the claimed value is too low.
(6 marks)
(Total 20 marks)
END OF EXAMINATION PAPER
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