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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) i) The contribution of matrices in the field of business and management is surely undoubted, state and briefly explain the areas of applications of matrices in business. (4 Marks) ii) A theatre charges 4 dollars for children and 8 dollars for adults. One weekend 100 people attended the theatre and the admission receipts totaled 6260 dollars. These can be represented by a matrix system, where x is the number of children and y is the number of adults attending. Find the number of children and adults attending. (4 Marks) b) Given the following transaction matrix Production sector Purchasing sector Consumer demand Agriculture Industry Agriculture 300 600 100 Industry 400 1200 400 i. Determine the input-output matrix. (3 Marks) ii. If the projected demand charges to 200 and 800 units respectively, what should be the gross output of each sector in order to meet the new demand? (4 Marks) c) A survey showed that 30% of university students pay their fees in full before the deadline. If 10 students were selected at random, determine the probability that; i. None will have paid in full. ii. Exactly three will have paid in full iii. Atleast one has paid in full. (6 Marks)
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d) Given that the marginal cost function for a certain product is MC = 3x +50and the fixed cost is Ksh. 100 per month. Find the total cost function, hence determine the cost of producing 10 items. (5 Marks) e) Distinguish between each of the following terms: i. Statistics and parameter ii. Type I and Type II errors. (4 Marks)
QUESTION TWO (20 MARKS) a) An economy depends on two basic commodities, wheat and oil. To produce 1 metric ton of wheat requires 0.25 metric tons of wheat and 0.33 metric tons of oil. The production of 1 metric ton of oil consumes 0.08 metric tons of wheat and 0.11 metric tons of oil. Find the production that will satisfy a demand of 500 metric tons of wheat and 1000 tons of oil. (7 Marks) b) Given that a firm has a total cost function given by the equation = 1 3 3 72 + 111 + 50 and the corresponding revenue function given by () = 100 2, determine the profit function and hence find the marginal profit when 20 units of the product are produced and sold. (7 Marks) c) i) When is it most appropriate to use a t-distribution? (2 Marks) ii) A random sample of size 16 has a mean of 54 and variance of 9. Determine the 95% confidence interval of the population mean. (4 Marks)
QUESTION THREE (20 MARKS) a) Maxwell Ltd as a result of past experience and estimates for the future has decided that the cost of production of their sole product E on an advanced process machine is given by the function = 1064 + 5 + 0.042 and sold. The marketing department has estimated that the price of the product is related to the quantity produced and sold by the equation = 157 3, where P = price per unit in sh. , E = quantity sold. Required: i. Determine the price and quantity that will maximize profits. (5 Marks) ii. Determine the price and quantity that will maximize revenues. (5 Marks) b) A certain concortion from Roriondo in Tanzania is claimed to be effective in curing colds. In an experiment on 164 people with cold, half of them were given the drug and half of the m given sugar pills (placebo). The patients reactions to the drug is recorded and the result below was obtained. Cured Harmed No effect Drug 52 10 20 Sugar pills 44 12 26 Test the hypothesis that the drug not better than Placabo. (Take = 0.05) (10 Marks)
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QUESTION FOUR (20 MARKS) a) Coopers Ltd, a company involved in the analysis of Human Resource carried a survey on the University Lecturers in public and private universities and reported the following. Each year 4% of the lecturers currently in public universities move to private universities. 6.5% of the lecturers currently in private universities move to public universities. At present 72% of the lecturers are in public universities. Assuming that the total population of the lecturers remains constant, what will be the distribution of lecturers two years from now? (8 Marks)
b) Determine the inverse of the matrix
1 2 2 3 1 4 3 2 1 . Hence solve the following
simultaneous equations + 2 + 2 = 4 3 + 4 = 25 3 + 2 = 4 (12 Marks)
QUESTION FIVE (20 MARKS) a) A company estimated the average lifespan of their refrigerator to be 6 years with a standard deviation of 1.2 years. i. Determine the probability of owning the refrigerator for (i) More than 3 years (3 Marks) (ii) Less than 4 years (3 Marks) (iii)Between 4 years and 7 years. (3 Marks) ii. If in a certain period 20% of the refrigerators were replaced for breaking down before t refrigerators. (4 Marks) b) Given the following data
Earning 000 sh 57 54 49 42 38 32 30 24 20 18 Saving 00sh 113 111 107 103 100 96 94 84 74 76
Calculate: i. Correlation coefficient ii. Coefficient of determination iii. Interpret the values in i) and ii). (7 Marks)
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