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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:2012
QUESTION ONE (30 MARKS) a) Briefly explain the following terms; i. Matrix ii. Marginal profits iii. Confidence intervals iv. Test of significance. (8 Marks) b) Let = 1 3 2 1 , = 4 5 1 6 = 1 3 5 4 . Show that + = + . (4 Marks)
c) Given that the total revenue function for a blender is = 36 0.012 where x is the number of units sold. Determine the average rate of change in revenue R(x) as x increases from 10 to 20 units. (4 Marks) d) A sample of 8 observations was taken from a population the sample mean was found to be 25 and sample found standard deviation 5. Determine a 95% confidence interval for the population mean. (5 Marks) e) A two segment economy consists of manufacturing and agriculture. To produce one unit of manufacturing output requires 0.40 units of its own output and 0.20 units of agricultural output. To produce one unit of Agricultural product requires 0.30 units of its own output and 0.40 units of manufacturing and 90 units of agriculture, what should be the output of each segment. (6 Marks)
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f) State three properties of a normal distribution. (3 Marks)
QUESTION TWO (20 MARKS) a) In a survey with a sample of 600 respondents the monthly income of the respondents follows a normal distribution with its mean and standard deviation as Kshs. 30,000 and ksh. 6,000 respectively. I. If a respondent is selected at random, determine the probabilities that the monthly income is; i. Less than Ksh. 24,000 ii. More than ksh. 32,000 iii. Between ksh. 20,000 and ksh. 34,000. (9 Marks) II. If 120 of the respondent surveyed were classified as poor. Determine the minimum monthly income a respondent should earn so as not to be in this class. (4 Marks) b) The total cost and the total revenue function for a product are: = 500 + + 0.52 and = 500 where q is the level of production. i. Using the marginal approach determine the profit maximizing level of output. (5 Marks) ii. What is the maximum profit? (2 Marks)
QUESTION THREE (20 MARKS)
a) A survey shows that 40% of invoices in a certain firm are erroneous. If 12 such invoices were sampled, determine the probabilities that: i. None was erroneous. (2 Marks) ii. At least 3 were erroneous. (3 Marks) iii. Exactly 3 were erroneous. (2 Marks) iv. All were erroneous. (2 Marks) v. At most 3 were erroneous. (2 Marks) b) Determine the inverse of the following matrix
1 2 2 3 1 4 3 2 1 Hence solve the simultaneous equations: + 2 + 2 = 4 3 + 4 = 25 3 + 2 = 4 (9 Marks)
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QUESTION FOUR (20 MARKS) a) A sociologist made a regional study of the shift of population between rural (R) and urban (U) areas. The transition matrix of the annual shift from one area to another was found to be R U R 0.76 0.24 U 0.08 0.92 Indicating that 76% of rural residents remains in rural areas, 24% move from rural to urban areas. 8% of urban residents move to rural areas and 92% remain in urban areas. Find the percentage of the population in rural and urban areas when the population stabilizes. (8 Marks)
b) A young company contracted to repair a bridge in a busy road section decided to carry a study on the potential of the section to cause an accident. They engaged in interviewing drivers passing through the temporary constructed bridge as they work on the permanent one. It was found out that the occurrence of an accident by passing traffic in a day is a random variable following a Poisson distribution with an average of three accidents in a day. Find the probabilities that in a certain day. i. At least three accident occurred. (4 Marks) ii. Exactly 5 accidents occurred. (3 Marks) iii. No accidents was reported. (2 Marks) c) State three characteristics of binomial distribution. (3 Marks)
QUESTION FIVE (20 MARKS)
a) Given the marginal profit function of a firm as = 200 4 Where x is the sales in units. If the firm breakeven on sales of 10 units. Find the fixed cost of the firm. (5 Marks) b) The mean life of a sample of 200 light tubes produced by a company is found to be 3160 hours with a standard deviation of 18 hours. Construct a 95% confidence interval of the mean. (5 Marks) c) Distinguish between correlation and regression. (4 Marks) d) The cost accountant of a firm producing solar panels has worked out the total cost function for the firm as = 120 2 + 0.023 . A sales manager has provided the sales forecasting function as = 114 0.25 where P is price and q the quantity sold. Determine;
The level of production that will yield minimum average cost per unit and determine whether this level of output maximizes profit for the firm. (6 Marks)
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