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) Graph sheet. (ii) Chi square and Normal Distribution tables. (iii) Formulas.
8 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. hypothetical counts that would occur if the alternative hypothesis were true b. hypothetical counts that would occur if the null hypothesis were true c. actual counts that occurred in a data set d. 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 c. 3.25 (b) 3.52 d. 3.31
3. What is the future value of K5,000 invested for 8 years at 12% compounded annually?
a. K15,813.68 c. K9812.82 b. K12,379.82 d. 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 c. 15.987 b. 18.307 d. 14.684
5. A feasible solution to a linear programming problem
a. must satisfy all the problem’s constraints simultaneously b. need not satisfy all of the problem constraints, only some of them c. must be a corner point of the feasible region. d. must give the maximum profit
6. One of the following is NOT a condition for the Binomial probability distribution
a. there are two possible outcomes called success and failure
A qualification examined by the Institute of Bankers in Malawi 2 b. there are n independent trials c. the probability of success is constant at each and every trial d. events occur in space or interval of time
7. Using the table of areas under the standard normal curve, find P1 z 2 where z ~ N0,1
a. 0.8185 c. 0.4772 b. 0.3413 d. 0.0618
8. Given that n 50 , x 30.2 and 5.1. Find the 95% confidence for the true population mean.
a. [28.2, 30.5] c. [25.3, 34.2] b. [29.3, 32.0] d. [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 Number of customers Khusa 118 Pamwamba 95 Wotsogola 102 Tilipo 135
9. To test the claim that preference for the bank is uniform, the null hypothesis would be stated as follows:
a. the level of preference for the bank is the same for each service station b. more customers prefer Tilipo bank c. the level of preference is not the same among the banks d. there is a difference between observed and expected sets of frequencies.
10.The expected frequencies for the bank are:
a. 118; 95; 102; 135 c. 450 each b. 112.5 each d. 150 each
11.Which one of the following is NOT a time series component?
A qualification examined by the Institute of Bankers in Malawi 3 a. control factors c. cyclic variation b. trend d. 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. Cannot be determined from the information given b. 0.167 c. 0.200 d. 0.833.
13.For the 90% confidence interval the critical z-value is
a. 1.965 b. 2.584 c. 1.645 d. 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. Paasche Price Index b. Financial times Index c. Retail Price Index d. 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. Payback b. Net Present Value c. Accounting Rate of Return d. None of the above.
16.The probability distribution of a random variable X is given in the following table.
X 1 2 3 4 5 6 P(X=x) 0.10 0.16 0.11 0.16 0.14 0.33
Find the mean of the given probability distribution.
A qualification examined by the Institute of Bankers in Malawi 4 a. 4.07 c. 0.17 b. 3.50 d. 3.94
17.Consider a linear programming problem with the objective function Maximize Z 50x 80y 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 c. 1400 b. 1480 d. 960
18.Given that, for the events A and B: nA 25 , nB 15 and nA B 10 , calculate PA | B.
a. 0.37 c. 0.57 b. 0.47 d. 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 2009 price (K) 2012 price (K) Weight Margarine 200 400 60 Cooking oil 1000 1200 20 Sugar 200 250 40
Calculate the weighted price index of the shop for 2012.
a. 1.62 c. 1.52 b. 1.89 d. 1.98
20.The following probability distribution is used when the sample size is small and the standard deviation is unknown;
a. Normal distribution b. t-distribution c. exponential distribution d. chi-squared distribution
SECTION B (60 MARKS)
A qualification examined by the Institute of Bankers in Malawi 5 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. (4 marks)
(b) (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:
A qualification examined by the Institute of Bankers in Malawi 6 (i) Exactly 2 of 8 customers are likely to default on loan repayment. (3 marks) (ii) 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. (2 marks) (ii) 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. (5 marks) ii. The percentage of customers with overdrafts of less than K41.000 (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 Project B Probability Profit (MK million) Probability Profit (MK million) 0.4 35 0.2 20 0.5 60 0.3 25 0.3 40 0.3 40 0.1 25 0.1 80 0.1 120
Which project would you choose and why? (5 marks) (Total 20 marks)
QUESTION 4
A qualification examined by the Institute of Bankers in Malawi 7 (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)
(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 Heating oil Jet fuel Light crude 0.3 0.2 0.3 Heavy crude 0.3 0.4 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)
A qualification examined by the Institute of Bankers in Malawi 8 (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? (3 marks)
(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 Account Type Level Savings Current Investment Fixed Primary 100 200 50 30 Secondary 300 400 80 70 Graduate 20 30 5 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) 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) (b) (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)
A qualification examined by the Institute of Bankers in Malawi 9 (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
A qualification examined by the Institute of Bankers in Malawi 10