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CPA Quantitative Analysis – December 2021 Past Paper & Answers

Unit: Quantitative Analysis

15 Questions

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Questions

Download CPA Quantitative Analysis December 2021 past paper with detailed answers and marking scheme. This paper is based on KASNEB examination standards and is ideal for revision and exam preparation.

Access the full paper online, download the PDF, or study offline. Each question includes step-by-step solutions to help you understand key concepts in Quantitative Analysis.

Other Quantitative Analysis Past Papers

1a
Time series
​​Explain the following terms as used in time series analysis:

(i) Cyclical variations.

(ii) Random variations.

(iii) Seasonal variations.

(iv) Trend. 

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1b
Time series
​ ​ ​ ​ ​ ​ ​ ​​The following data relates to the profits reported by XYZ Ltd. in each of the months in the year 2020:

Month
Profit (Sh."million")
January
40
February
38
March
39
April
41
May
36
June
41
July
34
August
37
September
35
October
37
November
40
December
41

Required: 

(i) Estimate the trend line using the ordinary least squares method. 

(ii) Estimate the profit reported in March of the year 2021.
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2a
Mathematical Techniques
​​ State five advantages of the arithmetic mean as a measure of central tendency.
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2b
Mathematical Techniques - Descriptive Statistics
​ ​ ​ ​ ​​The following data shows the distribution of profits of 150 manufacturing companies in a given year:

Profit ("Sh."million")
Number of companies
10-20
15
20-30
13
30-40
25
40-50
30
50-60
16
60-70
10
70-80
22
80-90
12
90-100
7

Required: 

(i) The arithmetic mean of the profits and interpret the results. 

(ii) The standard deviation of the profits and interpret the results. 

(iii) The coefficient of variation of the profits and interpret the results.
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3a
Linear programming
​​Explain the following terms as used in Markov analysis: 

(i) Markov process. 

(ii) Equilibrium state. 

(iii) Absorbing state. 

(iv) Closed state.
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3b
Linear programming
​ ​​The marketing department of Jacuzi Ltd. estimates the daily demand function of one of its products to be linear in nature. If the price was fixed at Sh.570, the daily demand would be 400 units. If the price was increased to Sh.820, the daily sales would drop to 200 units. 

The production department has indicated that the marginal cost of producing Q units of the product is given by the following equation:

MC = 2Q - 570 

Where: MC is the marginal cost and 
            Q is the number of units produced. 

The daily fixed cost is Sh.1,100. 

Required: 

(i) The revenue function of Jacuzi Ltd. 

(ii) The total cost function of Jacuzi Ltd. 

(iii) The maximum profit that Jacuzi Ltd. could make.
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4a
Hypothesis Testing and Estimation
​​In the context of hypothesis testing, distinguish between a "type I error" and a "type II error".
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4b
Hypothesis Testing and Estimation
​ ​ ​ ​​The sales before and after a promotional campaign in ten different regions for a certain commodity were recorded as follows:

Region
Sales before promotional campaign "Sh.million"
Sales after promotional campaign "Sh.million" 
1
53
58
2
28
29
3
31
30
4
48
50
5
50
50
6
42
45
7
63
59
8
40
36
9
25
22
10
30
28

Required: 
Using a 5% level of significance, determine whether the promotional campaign was a success or not. 
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5
Linear programming
​ ​ ​ ​​Bantu Limited makes two types of pudding: vanilla and chocolate. Each serving of vanilla pudding requires 2 teaspoons of sugar and 25 fluid measures of water, and each serving of chocolate pudding requires 3 teaspoons of sugar and 15 fluid measures of water. Bantu Limited has available each day 3,600 teaspoons of sugar and 22,500 fluid measures of water. Bantu Limited makes no more than 600 servings of vanilla pudding because that is all that it can sell each day. Bantu Limited makes a profit of Sh.10 on each serving of vanilla pudding and Sh.7 on each serving of chocolate pudding. 

Required: 

(a) Formulate a linear programming model to solve the above problem. 

(b) Construct an initial simplex tableau. 

(c) Using the simplex method, determine how many servings of each type of pudding Bantu Limited should make in order to maximise profit.
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6a
Mathematical Techniques
​​ State four applications of matrices in business.
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6b
Probability
​​A global conference on "the blue economy" was recently held in Kenya and was attended by 280 delegates from America, Europe and Africa.

The following information relates to the delegates who attended the conference:

  • 70 delegates represented Europe
  • 96 delegates represented Africa
  • 128 delegates represented America
  • 20 delegates represented all the three continents.
  • 25 delegates represented America and Africa
  • 22 delegates represented America and Europe
  • 26 delegates represented Europe and Africa
Required:

(i) Present the above information in the form of a Venn diagram.

(ii) The number of delegates who represented at least two continents.

(iii) The number of delegates who represented only one continent.

(iv) The number of delegates who represented none of the three continents.
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6c
Probability
​ ​​During the manufacture of a product, 0.002 of the product turns out to be defective. The product is supplied in packets of 10. A consignment of 100,000 packets is produced in a certain period.

Required:

Using the Poisson distribution, calculate the approximate number of packets containing:

(i) No defectives.

(ii) 1 defective.

(iii) 2 defectives.

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7a
Hypothesis Testing and Estimation
​ ​​A random sample of 15 employees of a call centre was taken and each employee took a competency test. The mean of the scores achieved by these employees was 56.3% with a standard deviation of 7.1%. The results ofthis test have been found to be normally distributed in the past. 

Required: 

Construct a 95% confidence interval for the mean of the test score of the call centre employees.
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7b(i)
Correlation and Regression Analysis
​​Distinguish between the "coefficient of correlation" and the "coefficient of determination".
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7b(ii)
Correlation and Regression Analysis
​​ The following data was obtained during a social survey conducted in a given urban area regarding the monthly income of households and their corresponding expenditure:

Household
Monthly income
 Sh."000" 
Monthly expenditure
 Sh."000" 
A
150
120
B
130
135
C
200
195
D
245
190
E
140
120
F
100
85
G
80
65
H
145
130
I
130
60
J
90
75

Required: 

The Pearson's coefficient of correlation between monthly income and monthly expenditure and interpret result.
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