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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. 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 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? Justify your response. (3 marks) 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