Hps2205:Quantitative Methods Question Paper
Hps2205:Quantitative Methods
Course:Bachelor Of Commerce
Institution: Meru University Of Science And Technology question papers
Exam Year:2013
QUESTION ONE – (30 MARKS)
(a) Highlight the significance of mathematics in business and management. (3 Marks) (b) Solve the following
4 1
2
1
3
1 1 ? ? ?? ? xx
(4 Marks)
(c) A woman group decided to raise Ksh.480,000 to start a business venture. Before the actual payment was made, four of the members pulled out and each of those that remained had to pay an additional Ksh.20,000. Determine the original number of members. (5 Marks) (d) Distinguish between each of the following terms. (i) Discrete and continuous variable (ii) Sample and population. (4 Marks) (e) A professional football player feels that his playing career will last for the next 8 years. To prepare for his future, he deposits Ksh35000 at the end of each year for 8 years in an account paying 12% interest compounded annually. Determine the amount he will have in his account at the end of 8 years. (4 Marks) (f) Given the following data set 6, 5, 11, 7, 15, 10, 8, 7, 12 Determine (i) Mode (1 Mark)
2
(ii) Median (2 Marks) (iii) Arithmetic mean (2 Marks) (iv) Geometric mean (2 Marks) (g) Explain the following terms as used in set theory (i) Mutually disjoint set (1 Mark) (ii) Universal set (1 Mark) (iii)Compliment of a seat (1 Mark)
QUESTION TWO – (20 MARKS)
(a) The table below shows the age (in years) of people ferried by a bus company to work one morning Age 10 -19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 – 79 80 - 89 No. of people 37 59 156 172 143 75 32 10
Using the data, determine (i) The modal class (ii) Construction a frequency table and use it to calculate the mean, median and standard deviation (9 Marks) (iii)On the same axis, represent the data using a histogram and frequency polygon curve. (3 Marks) (iv) Using the histogram drawn in (iii) estimate the mode. (1 Mark) (v) Calculate the Karl Pearson coefficient of skewness and comment on the distribution of the data. (3 Marks) (b) State three properties of a good measure of central tendency. (3 Marks)
QUESTION THREE – (20 MARKS)
(a) The Beta Co. Ltd is considering the purchase of a new machine. Two alternative machines A and B have been suggested each costing Sh.400,000. Earning after taxation are expected to be as follows (Cash flows)
CASH FLOWS Year Machine A Machine B 1 40,000 120,000 2 120,000 160,000 3 160,000 200,000 4 240,000 120,000 5 160,000 80,000
3
The company has a target of return on capital of 10% (i) Compute the net present value (NPV) and the profitability index of each machine. (10 Marks) (ii) State which machine you consider financially preferable. (1 Marks) (b) The demand function for a given commodity is given by ?? = 420 - 0.2?? and the supply function is given by ?? = 60 + 0.4??. Determine the product equilibrium point for this product. (4 Marks) (c) Consider the following sets = 2,3,4,5,6,7,8,9, = 1,2,5,7,9,10,11,12 ?? = 1,5,7,8,9,10,11,12,13 = :1 15
Determine (i) ?? (2 Marks) (ii) ??/ (2 Marks)
QUESTION FOUR – (20 MARKS)
(a) Explain the concept business appraisal and discuss two significance of carrying out business appraisals. (6 Marks) (b) The mail daily newspapers in Nyeka; the National, the New Era and the Citizen. The management of the dailies is concerned about the low sales volume of their papers. In recent survey of 200 families in Nyeka on the numbers that read the various news papers were found to be as follows: Newspapers number of readers The Citizen 56 Citizen and New Era 16 The New Era 60 Citizen and National 20 New Era and National 10 National 84 All the three newspapers 6
(i) Present the information in a Venn diagram (4 Marks) (ii) Determine the number of families who did not read any of the three newspapers. (2 Marks) (iii)Determine the number of people who read atmost two newspapers. (2 Marks)
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(c) The consumption of electricity has increased historically at 6% per year. If it continued to increase at this rate indefinitely, find the number of years before the electricity utilities would need to double generating capacity. (6 Marks) QUESTION FIVE – (20 MARKS)
(a) The following data relates to the distribution of 150 workers in terms of sex, mean monthly saving and standard deviation. Sex No. of employees Monthly average savings Standard deviation Male 100 5000 50 Female 50 8000 85
(i) Determine the combined mean. (4 Marks) (ii) Calculate the coefficient of variation for each sex and state which group has more variability in savings. (7 Marks) (b) There are three urns one black containing 3 re and 7 white marbles, one red containing 4 yellow marbles and 6 green marbles and one white containing 8 yellow and 2 green marbles. A marble is first drawn from the urn. A second marble is then drawn from the urn having the same colour as the first marble drawn. If the second marble is yellow. Determine the probability that the first marble was read. (5 Marks) (c) Determine what you would pay for an annuity which promises Ksh.9000 a year for the next 10 years given an interest rate of capital at 8 %. (4 Marks)
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