KASNEB Quantitative Analysis - Question 2b

The time taken to complete a particular task was measured for 250 workers and the results were as shown below: Time taken in minutesNumber of workers0 ... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 5a

Outline FOUR properties of a set. ... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 6b

The quarterly profits of Nyota Limited during the years 2019, 2020, and 2021 were as tabulated below: Profits in Sh.“million”Year Quarter 1 Qua... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 7b

A linear programming problem has been formulated as below:Objective function: Max Z = 14x + 10ySubject to:1. 4x + 3y ≤ 2402. 2x + y ≤ 1003. y ≤ 504. ... [Click to view full question and step-by-step solution]

April 2023

Q: KASNEB Quantitative Analysis - Question 4a

Differentiate between the following terms:(i) “Coefficient of skewness” and “coefficient of variation”.(ii) “Arithmetic mean” and “harmonic mean”.... [Click to view full question and step-by-step solution]

1a

Probability

A survey was conducted to establish the number of faulty components from a production process. The results indicated that 0.01% of the components produced were faulty. Each machine produces 10,000 components.

Required:

The probability of there being 3 or more faulty components assuming a Poisson probability distribution.

1b

Mathematical Techniques

The Sales Manager of XYZ Ltd. estimates that the revenue function of the company is linear in nature. He has observed that at a selling price of Sh.200, the company sold 6,000 units. When the company increased the selling price per unit to Sh.700, the company sales decreased to 1,000 units.

The Cost Accountant of the company estimates that the cost function is quadratic in nature. The following data was provided:

Number of units (Q)	100	200	400
Total cost (Sh.) TC	79,000	76,000	124,000

Required:

(i) The revenue function.

(ii) The total cost function.

(iii) The profit maximising level of production.

2a

Probability

A survey was recently conducted to determine the preferences of 360 customers with regard to three brands of cooking oil namely; sunflower oil, coconut oil and olive oil.

The following results were obtained:

220 customers preferred sunflower oil.
160 customers preferred coconut oil.
180 customers preferred olive oil.
80 customers preferred both sunflower oil and coconut oil.
110 customers preferred both sunflower oil and olive oil.
100 customers preferred both coconut oil and olive oil.
50 customers preferred none of the brands of cooking oil

Required:

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

(ii) Determine the probability that a customer picked at random prefers all the three brands of cooking oil.

(iii) Determine the probability that a customer picked at random prefers at least two brands of cooking oil.

2b

Mathematical Techniques - Descriptive Statistics

The time taken to complete a particular task was measured for 250 workers and the results were as shown below:

Time taken in minutes	Number of workers
0 – 5	2
5 – 10	2
10 – 15	3
15 – 20	5
20 – 25	5
25 – 30	18
30 – 40	X
40 – 50	100
50 – 60	Y
Above 60	15

Required:

(i) Determine the value of X given that the median time taken to complete the task is 40.5 minutes.

(ii) Determine the value of Y given that the modal time taken to complete the task is 41.5 minutes.

3a

Mathematical Techniques - Matrix Algebra

Using the information given below, determine the level of output necessary from each sector to support a final demand of 500 units for sector X1, 1,600 units for sector X2 and 2,000 units for sector X3:

	Inputs to
Output	\(X_1\)	\(X_2\)	\(X_3\)	Final demand (units)
\(X_1\)	40	40	40	680
\(X_2\)	40	80	80	1,400
\(X_3\)	400	1,200	280	2,120

3b

Hypothesis Testing and Estimation

The monthly rent paid by residents of Hill View Estate is found to be normally distributed with a mean of Sh.22,150 and a standard deviation of Sh.8,900.

Required:

On the basis of a sample of 200 residents:

(i) Construct a 95% confidence interval for the monthly rent paid.

(ii) Test the hypothesis that the amount paid in monthly rent is Sh.20,000 at a 5% significance level

4a

Mathematical Techniques - Descriptive Statistics

Differentiate between the following terms:

(i) “Coefficient of skewness” and “coefficient of variation”.

(ii) “Arithmetic mean” and “harmonic mean”.

4b

Correlation and Regression Analysis

Mr Rajab Omar is the Marketing Manager of Tintex Limited. He gathered data on the number of sales people engaged in a month and the sales made in the last ten months of the year 2022.

The results were as follows:

Year 2022 Month	Number of sales people engaged	Sales Sh.“000”
March	12	23
April	11	22
May	14	23
June	12	24
July	15	28
August	11	22
September	13	23
October	14	26
November	10	20
December	9	17

Required:

(i) Estimate the total sales function using the ordinary least squares method.

(ii) Predict the sales made in the month of January 2023 when 19 sales people were engaged.

5a

Decision Theory

Outline FOUR properties of a set.

5b

Mathematical Techniques - Matrix Algebra

A trader purchased 7 cartons of apples and 4 cartons of bananas at a total cost of Sh.32,500 in the month of January.In the month of February, he purchased 9 cartons of apples and 6 cartons of bananas at a total cost of Sh.43,500.

Required:

Calculate the cost of a carton of apples and a carton of bananas using matrix algebra

5c

Decision Theory

Red Rose Limited has developed a new washing detergent. The company is considering whether or not to market test the detergent prior to its launch. Market testing will cost Sh.50 million which may increase the likelihood of success of the product if it passes the test. The probability of passing the test is 0.8. If the product fails the test, it is regarded as worthless.

Previous data collected was as follows:

Probability of	No testing	Market testing
High success	0.20	0.40
Moderate success	0.35	0.40
Low success	0.45	0.20

Launching the product will cost Sh.150 million and the estimated profits are as follows:

High success	Sh.900 million
Moderate success	Sh.450 million
Low success	Sh.225 million

Red Rose Limited has the option of selling the product design for Sh.250 million.

Required:

(i) A decision tree showing the pay-off and the expected monetary value (EMV) of each decision.

(ii) Advise the management of the company on the best course of action and the related expected monetary value (EMV).

6a

Time series

In the context of time series analysis, distinguish between the following terms:

(i) “Mean absolute deviation” and “mean squared error”.

(ii) “Additive model” and “multiplicative model”

6b

Time series

The quarterly profits of Nyota Limited during the years 2019, 2020, and 2021 were as tabulated below:

	Profits in Sh.“million”
Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
2019	105	138	116	140
2020	104	122	103	146
2021	113	149	141	162

Required:

(i) The three-quarter moving averages.

(ii) The seasonal index for each quarter assuming the multiplicative model.

(iii) Derive the deseasonalised profits using the multiplicative model.

7a

Probability

Explain the meaning of the following terms in the context of probability theory:

(i) Mutually exclusive events.

(ii) Independent events.

7b

Linear programming

A linear programming problem has been formulated as below:

Objective function: Max Z = 14x + 10y

Subject to:	1. 4x + 3y ≤ 240
	2. 2x + y ≤ 100
	3. y ≤ 50
	4. x, y > 0

Required:

(i) Optimal production for x and y using the simplex method.

(ii) The slack values for each constraint.

(iii) The shadow price for each constraint.

April 2023

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