Syllabus
CPA PART II  SECTION 4
PAPER NO.11 QUANTITATIVE TECHNIQUES
OBJECTIVE
To provide the candidate with quantitative techniques for use in solving
managerial problems.
11.0 SPECIFIC OBJECTIVES
A candidate who passes this subject should be able to:

TOPIC 2
QUESTION 1
a)
i)
Sector
Weight
W
Summati
on
Mining and quarrying 41
July
2001
Index (1994
= 100)
P
WP
361
41
Summati
on
1480
1 14801
Manufacturing:
Food,
drink
tobacco
and 77
106
8162
Chemicals
66
109
7194
Metal
47
72
3384
Engineering
298
86
2562
QUESTION 9
a) The sets can be presented as below:
i)
A Simiyu , Juki , Waithera , Baraza, Thuo , Mwanzia
C Simiyu , Macharia , Waithera , Kungu, Thuo, Mwanzia
D Simiyu , Baraza,
ii) The Venn diagram showing these set is as follows:
Universal set
D
A
Bar
= 0.05 then the test statistic is
Z
x
16.5 15
6.046 1.96
s
3.5
n 1
200 1
H0 is rejected and H1 is accepted. The average number of weekly sales contact
per sales representative has changed significantly.
From normal distribution tables for two tailed te
PROBABILITY
QUESTION ONE
A problem is given to three managers A, B, C whose chances of solving are ,
, respectively. What is the probability that the problem will be solved?
QUESTION TWO
Three groups of children contain respectively 3 girls and 1 boy; 2 g
0
0.05
0.95 0
0
0 .1
0 .2 0 .7
A B C D
A B C D
0
0.2 0.65 0.15
0
0
0.2 0.8
and A + B + C + D = 1
(1)
(2)
From the matrix multiplication (1), the following expressions are
determined in terms of A.
0.95 A + 0.2 B = A 0.05 A = 0.2 B
(3)
B = 0.25
Introduction
1
Part I: Introduction
How To Use This Revision Kit
Questions and answers have been presented following from the structure of the
quantitative techniques paper. Looking at the chapter arrangement the structure
can be seen. After getting the c
a) Summarize the procedure for solving the kind of quantitative technique you
have used to solve part (a) above.
(Q 6 June 2001)
QUESTION EIGHT
a) A small company will be introducing a new line of lightweight bicycle
frames to be made from special alumini
9.472
10 x 2 x 3
5x
3
0.527
2
=
3
9.472
2
5 9.472
5 9.472
3
3
0.527
2
5 0.527
5 0.527
3
= 117.96 ( 1.30) = 119.26 1000
= Sh. 119,260
QUESTION 5
a)
i) To obtain the time when there are a maximum number of people
queuing, the derivative of t
QUESTION FOUR
An endowment fund manager is attempting to determine a best investment
portfolio and is considering six alternative investments. The following table
indicates point estimates for the price per share, the annual growth rate in the
price per s
1250000.01625000030000=32,500
So the difference in profit is 32,500(30000)=62,500
QUESTION 9
a) The Leontief open model is
Mx+d=x
So rearranging the equation
(IM)x=d
x=(IM)1d
Where Mmatrix of technical coefficients
xrequired production
dthe exte
Order
type
Consuma
bles
Sales
Purchas
e
Producti
on
Account
s
Maintenanc
e
Total
10
12
4
8
4
38
Equipmen
t
1
3
9
1
1
15
Special
0
0
4
1
2
7
11
15
17
10
7
60
Total
An error has been found in one of these orders.
Required:
i) Determine the probability that
QUESTION NINE
a) Given the following input output matrix and demand vector of shoes S,
rubber R and glue G industries, determine the production vector.
Input output matrix
S
R G
S 0.3
R 0.1
G
0.2
Demand vector
0.2
0.4
0.3
0.1
0.2
0.4
40
50
60
DECISION THEORY
QUESTION ONE
The following is a payoff table for a particular venture.
States of nature
1
2
3
4
5
D1
150
225
180
210
250
Decision
D2
180
140
200
160
225
Alternatives
D3
220
185
195
190
180
D4
190
210
230
200
160
Determine the optimal decis
a) Kenya Canning Transport is to move goods from three factories situated in
thika, Naivasha and Machakos. These goods will be distributed to Nairobi,
Mombasa and Kisumu. Informaion about the units (in kilograms) to be
moved is given below:
Factory
Supply
Acknowledgment
We gratefully acknowledge permission to quote from the past examination papers of
the following bodies: Kenya Accountants and Secretaries National Examination Board
(KASNEB); Chartered Institute of Management Accountants (CIMA); Association
QUESTION THREE
a) A machine produces circular bolts and, as a quality control test, 250 bolts
were selected randomly and the diameter of their heads measured as
follows:
Diameter
(cm)
of
head
Number
components
0.9747 
0.9749
2
0.9750 
0.9752
6
0.9753 
SAMPLING & ESTIMATION
QUESTION ONE
Suppose it is known that the mean annual income of workers in a certain
community is Rs.5,000 with a standard deviation of Rs.1,200. A researcher
suspects the son of soil workers have higher than the average income. He
d
Topical Guide to Past Paper Questions
Chapters arranged according to exam question flow
Topic 1
Linear algebra, matrices algebra application, calculus and
set theory
Topic 2
Measures of central tendencies, measures of dispersion
and index numbers
Topic 3
QUESTION SEVEN
a) Mia Shillings Department Stores is planning to open a store in Westlands. It
has asked the Superior Marketing Company (SMC) to do a market study of
randomly selected families within a fivekilometer radius of the store.
Among the questio
Standard error of the regression line
x
2
i
nx 2
and where the standard error of the regression line is:
(y
y ) 2
n 2
i
You are required to:
a) Plot the original data on a graph, calculate the least squares regression of y
on x and draw the regression
QUESTION SEVEN
a) Define the following terms used in game theory:
i) Dominance.
ii) Saddle point
iii) Mixed strategy
iv) Value of the game
b) Consider the two person zero sum game between players A and B given by
the following payoff table:
Player A Stra
QUESTION THREE
Consider the costtime estimates for the product development project of
question one above as given in the table below.
Time Estimates (weeks)
Activity
Normal
Crash
Direct Cost Estimates ($
000)
Normal
Crash
A
3
1.0
3.5
10.0
B
1
0.5
1.2
2.0
Revision Questions and Answers
1
QUESTION SEVEN
a) State four attributes of the Beta distribution which made it to be chosen as
representing the distribution of activity times in project evaluation and review
technique (PERT).
b) Lillian Wambugu is the pr
a)
i)
This is a Poisson distribution since there is a given rate, which is a mean
for vehicles passing. In a large interval, the number of vehicles passing
is scattered. The interval is small.
ii) The mean number of vehicles passing per 20 second interval
a=
y b x 156.643 0.0393 171 5.1556
n
n
18
18
So, T = 5.1556 + 0.0393 Quarter number
QUESTION 8
a)
i)
Month
No. (t)
Jobs Y
t
Yt
March
1
353
1
353
April
2
387
4
774
May
3
342
9
1026
June
4
374
16
1496
July
5
396
25
1980
August
6
409
36
2454
September
7
399
This side from Spiceland use with the 1st lecture
Sales discounts.
Harwell Company manufactures automobile tires. On July 15, the company sold 1,000 tires to
the Nixon Car Company for $50 each. The terms of the sale were 2/10, n/30. Harwell uses
the gross