KASNEB Quantitative Analysis - Question 1b

The following data relates to the profits reported by XYZ Ltd. in each of the months in the year 2020: MonthProfit (Sh.'million')January40Febru... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 2a

State five advantages of the arithmetic mean as a measure of central tendency. ... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 2b

The following data shows the distribution of profits of 150 manufacturing companies in a given year: Profit ('Sh.'million')Number of companies10-2015... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 4a

In the context of hypothesis testing, distinguish between a 'type I error' and a 'type II error'. ... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 6a

State four applications of matrices in business. ... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 7b(i)

Distinguish between the 'coefficient of correlation' and the 'coefficient of determination'. ... [Click to view full question and step-by-step solution]

December 2021

1a

Time series

Explain the following terms as used in time series analysis:

(i) Cyclical variations.

(ii) Random variations.

(iii) Seasonal variations.

(iv) Trend.

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.

2a

Mathematical Techniques

State five advantages of the arithmetic mean as a measure of central tendency.

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.

3a

Linear programming

Explain the following terms as used in Markov analysis:

(i) Markov process.

(ii) Equilibrium state.

(iii) Absorbing state.

(iv) Closed state.

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.

4a

Hypothesis Testing and Estimation

In the context of hypothesis testing, distinguish between a "type I error" and a "type II error".

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.

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.

6a

Mathematical Techniques

State four applications of matrices in business.

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.

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.

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.

7b(i)

Correlation and Regression Analysis

Distinguish between the "coefficient of correlation" and the "coefficient of determination".

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.

December 2021

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