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Mbad 681: Quantitative Methods Question Paper
Mbad 681: Quantitative Methods
Course:Master Of Business Administration
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
EXAMINATION FOR THE AWARD OF DEGREE OF
MASTER OF BUSINESS ADMINISTRATION
MBAD 681: QUANTITATIVE METHODS
STREAM: MBA Y1S1 TIME: 3 HOURS
DAY/DATE: TUESDAY 13/8/2013 5.30 P.M. – 8.30 P.M.
INSTRUCTIONS:
Answer FOUR questions. Each question carries 25 marks.
Do not write on the question paper.
QUESTION ONE: (25 MARKS)
Outline the advantages of the study of statistics. [5 marks]
State the properties of the Normal distribution. [5 marks]
The quality controller in a given firm observes that the average weight of 2000 units produced in a workshop (per day) is 130kg with a variance of 100kg. Assuming normal distribution, how many units are expected to weight less than 142 kg?
[3 marks]
The table below shows the distribution of iron bar lengths produced in a factory in December 2012.
Bar lengths (cm) No. of bars
201 – 250 25
251 – 300 36
301 – 350 49
351 – 400 0
401 – 450 51
451 – 500 42
501 - 550 30
Calculate the standard deviation of the lengths of the bars. [5 marks]
Test the normality of the distribution by comparing the proportion of the cases lying between ¯X±1s ; ¯(?X)±2s and ¯X±3s for the above statistics.
[7 marks]
QUESTION TWO: (25 MARKS)
If A = {p, q, r, s}, B = {q, r, t, v} and C = {r, s, v, w}
Verify that:
A-(BnC)=(A-B)?(A-C) [3 marks]
A-(B?C)=(A-B)n(A-C) [3 marks]
Out of 450 students who appeared for CIMA examination in a centre, 135 failed in Accounting, 150 failed in Modeling and 2137 failed in Computer. Those who failed in both Accounting and Modeling were 93, in Modeling and Computer were 98 and in Accounting and Computer 106. The number of students who failed in all the three units were 75. Assume that a student appeared in each of the three units.
Required:
Find the number of those who failed in at least one of the three units. [4 marks]
Find the number of those who passed in all the three units. [1 mark]
What is the probability that a student picked at random failed in
mathematics only. [2 marks]
Suppose you are interested in using past expenditure on research and development to predict current sales. You got the following data by taking a random sample of 12 firms where X is the amount of expenditure on research and development (in KSh. million) and Y is the amount of sales in (KSh. million)
X: 9 19 11 14 23 12 12 22 7
Y: 15 20 14 16 25 20 20 23 14
X: 13 15 17
Y: 22 18 18
Required:
Find out the regression equation of sales on advertising expenditure. [5 marks]
Project the sales when advertising expenditure are Sh. 10,000,000. [1 mark]
Compute the coefficient of determination (R2) and interpret your result.
[4 marks]
Compute the standard error of the estimate (Se) and interpret your result.
[3 marks]
QUESTION THREE: (25 MARKS)
Solve the following system of simultaneous equations by any suitable method.
?4x?_1+?5x?_2-?2x?_3=18
x_1+x_2-x_3=4
? 9x?_1+?11x?_2-?5x?_3=20 [6 marks]
Outline the input-output analysis of intersectoral relations highlighting the factors
that differentiate the open and closed system. [4 marks]
A simple society economy consists of coal production, oil and transport sectors. 60% of each unit of coal output goes towards coal production, 10% towards oil and the rest towards the transport sector.The output from the oil sector is shared among the three sectors – coal, oil and transport in the ratio 3:5:2 respectively.20% of the output from transport sector is distributed to coal, 10% towards oil sector and the rest towards the transport sector. Given that the external demand for the output from coal, oil and transport sectors are respectively 600 units, 1500 units and 900 units. Find:
The technological matrix (M). [2 marks]
Find (1 – M)-1 [4 marks]
The output from each sector. [3 marks]
Suppose in a monopoly market, the total cost per week for producing a product is given by C = 3600+100x+?2x?^2. Suppose further that the weekly demand function for this product is P=500-2x. Find the number of units that will break even the product.
[5 marks]
QUESTION FOUR (25 MARKS)
What is the meaning of decision theory? Explain elements of the decision environment.
[5 marks]
A manufacturing firm purchases a certain component for its manufacturing process from three sub-contractors A, B and C. These supply 60%, 30% and 10% of the firm’s requirements respectively. It is known that 2%, 5% and 8% of the items supplied by the respective suppliers are defective.
On a particular day, a normal shipment arrives from each of the three suppliers and the contents get mixed. A component is chosen at random from the day’s shipment.
What is the probability that it is defective? [3 marks]
If this component is found to be defective, what is the probability that it was supplied by
A (ii) B (iii) C [6 marks]
Before an increase in duty, 400 people were alcohol drinkers in a sample of 500 people. After an increase in duty, 400 people were found to be alcohol drinkers in a sample of 600. Test at 5% level of significance whether there is a significant increase in the consumption of alcohol. [4 marks]
An insurance company takes keen interest in the age at which a person is insured. Consequently, a survey conducted on prospective clients indicated that for clients having the same age, the probability that they will be alive in 30 years time is . This probability was established using actuarial tables. If a sum of 5 people were insured now, find the probability of having the following possible outcomes in 30 years.
All are alive [2 marks]
At least 3 are alive [2 marks]
At most one is alive [2 marks]
None is alive [2 marks]
QUESTION FIVE: (25 MARKS)
(i) Given ¯MR=300-0.2X where X represents quantity sold, find the Total
Revenue function. [3 marks]
(ii) Find the minimum value of the function Z=x^3+y^3+xy subject to
x+y=4. [5 marks]
(i) Highlight the advantages of linear programming approach to decision making.
[5 marks]
Three products A, B and C are produced at three machine centres X, Y and Z. Each product involves operation of each of the machine centres. The time required for each operation of various products is indicated in the following table:
Machine Centres Profit/Unit
Product X Y Z Sh.
A 10 7 2 12
B 2 3 4 3
C 1 2 1 1
Available hours 100 77 80
Required:
Formulate a linear programming problem on the basis of the given information.
[4 marks]
Find out suitable product mix so as to maximize profit. [7 marks]
How many hours are surplus in Machine Centre? [1 mark]
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