KASNEB Quantitative Analysis - Question 2b

The following data shows the age distribution of 350 employees of a multi-national company. Age (years)Number of employees20-252025-30 7030-35100... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 3b

The following information relates to the operating life of two brands of mobile phones, brand A and brand B: Brand ABrand BMean life (days)1,7301,684Stan... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 6a(i)

Highlight four requirements that must be met before the linear programming model can be applied. ... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 6b

State any four assumptions of the Poisson probability distribution. ... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 7a

The table below shows the quarterly profits of Kahawa Limited (in millions of shillings) for the years 2019, 2020 and 2021: Quarterly profits (Sh.'mi... [Click to view full question and step-by-step solution]

April 2022

1a

Mathematical Techniques

Hexadol Limited has been in operation for the last 5 years. The Company's annual revenue function and annual cost function take the form of quadratic functions.

The following data was obtained from the records of the company for the last 3 years:

	Year
	2019	2020	2021
Units produced and sold: “million"	4	8	12
Revenue Sh."million"	2,320	4,480	6,480
Cost Sh."million"	10,404	9,832	9,272

Required:

(i) The revenue function of the company.

(ii) The cost function of the company.

1b

Probability

Explain the following terms as used in probability:

(i) Joint probability.

(ii) Mutually exclusive events.

(iii) Conditional probability.

(iv) Dependent events.

1c

Probability

A firm has 500 employees out of whom, 2% have a minor accident in a given year. Out of the employees who have a minor accident in a given year, 30% had safety instructions. 80% of all employees had no safety instructions.

Required:

The probability of an employee being accident free given that the employee had no safety instructions.

2a

Mathematical Techniques

Explain three types of Kurtosis that a graphical representation of a frequency distribution can assume.

2b

Mathematical Techniques

The following data shows the age distribution of 350 employees of a multi-national company.

Age (years)	Number of employees
20-25	20
25-30	70
30-35	100
35-40	65
40-45	40
45-50	25
50-55	15
55-60	10
60-65	5

Required:

Compute the following measures and give an interpretation of each:

(i) The mean age.

(ii) The median age.

(iii) The standard deviation of the employees' ages.

(iv) The Karl Pearson's coefficient of skewness.

3a

Hypothesis Testing and Estimation

A random sample of 350 invoices issued by ARIK Ltd. revealed an average invoice value of Sh.38,780 with a standard deviation of Sh.8,750.

Required:

(i) The interval within which the population mean should fall at 95% level of confidence.

(ii) The sample size of invoices that would result in a 99% confidence level of the interval obtained in (a) (i) above.

3b

Hypothesis Testing and Estimation

The following information relates to the operating life of two brands of mobile phones, brand A and brand B:

	Brand A	Brand B
Mean life (days)	1,730	1,684
Standard deviation (in days)	102	108
Sample size	200	200

Required:

Advise a potential customer on whether there is any significant difference between the quality of the two brands of mobile phones at a 5% level of significance.

3c

Hypothesis Testing and Estimation

A certain new strategy K was claimed to be effective for teams playing a certain game.

In a marathon of 400 games, half of the teams used strategy K and the other half used strategy P.

The teams' performance was recorded in the following table

	Won	Defeated	Drawn
Adopted strategy K	130	20	60
Adopted strategy P	110	30	50

Required:

On the basis of the above data and using the chi-square method, advise whether there is a significant difference in the effect of the two strategies, K and P.

4a

Mathematical Techniques

XYZ Ltd. produces three products namely A, B and C. The company presents the profit per unit of the products it produces and sells as follows: Sh.2,000, Sh.3,000 and Sh.4,000 for products A, B and C respectively during the month of January 2022. Sh.7,000, Sh.9,000 and Sh.4,000 for products A, B and C respectively during the month of February 2022. Sh.1,000, Sh.4,000 and Sh.2,000 for products A, B and C respectively during the month of March 2022. The total profits in the months of January, February and March 2022 are Sh.17 million, Sh.45 million and Sh.16 million respectively.

Required:

The total number of each product produced and sold using matrix algebra.

4b

Probability

The savings accounts in a certain microfinance bank have an average balance of Sh.240,000 and a standard deviation of Sh.60,000. The account balances are assumed to be normally distributed.

Required:

(i) The proportion of savings accounts whose balances are above Sh.275,000.

(ii) The proportion of savings accounts whose balances lies between Sh.190,000 and Sh.260,000.

4c

Mathematical Techniques

The average revenue function of a certain company is given by the function AR = 2,000 - 24q. The cost function is given by the function C = 6q² + 1,440q + 1,280. In both cases, q represents the quantity in units.

Required:

(i) The profit function of the company.

(ii) The maximum profit for the company.

5

Correlation and Regression Analysis

Ahadi Ltd. is in the process of analysing its electricity expense and its relationship with the machine hours of operation.

The following data is provided with respect to the year ended 31 December 2021:

Month	Number of machine hours "000"	Electricity expense "000"
January	72	1,020
February	55	820
March	39	720
April	60	900
May	49	870
June	39	720
July	53	825
August	81	1,365
September	63	870
October	59	890
November	45	790
December	50	940

Required:

(a) The least squares regression line for the above data and interpret its meaning.

(b) Estimate the amount of electricity expense assuming the expected machine hours are 78,000.

(c) The product moment correlation coefficient between machine hours and electricity expense. Interpret your answer.

(d) The standard error of estimate for the regression line. Interpret your answer.

6a(i)

Linear programming

Highlight four requirements that must be met before the linear programming model can be applied.

6a(ii)

Linear programming

A company makes two products; 1 and 2.

Each product requires time on two machines A and B. The specifications for each product are as follows:

	Product 1	Product 2
Processing time:
Machine A (Hours/unit)	1.6	1.0
Machine B (Hours/unit)	2.5	1.0
Selling price (Sh./unit)	22	48
Material and labour cost (Sh./unit)	14	37
Maximum possible production and sale (units)	30	50

Maximum time available for machine A is 80 hours and for machine B is 100 hours.

Required:

Formulate a linear programming model to determine the number of product 1 and product 2 which should be produced and sold in order to maximise total contribution for the company using the graphical method.

6b

Probability

State any four assumptions of the Poisson probability distribution.

7a

Time series

The table below shows the quarterly profits of Kahawa Limited (in millions of shillings) for the years 2019, 2020 and 2021:

	Quarterly profits (Sh."million")
Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
2019	23	32	27	21
2020	27	35	32	24
2021	31	43	40	29

Required:

(i) The three-quarter moving average of the profits.

(ii) The quarterly seasonal variations of the profits using the additive model.

(iii) Forecast the adjusted profits for the year 2022 given that the actual profits (in Sh."million") in the year 2022 are 35, 50, 47 and 33 for Quarter 1, Quarter 2, Quarter 3 and Quarter 4 respectively.

7b

Decision Theory

An investment manager in an investment fund has a choice between:

1. A diversified portfolio promising Sh.15 million with a probability of 0.7 and Sh.8 million with a

probability of 0.3.

2. A risky investment consisting of two contracts with independent outcomes one promising Sh.7 million with a probability of 0.7 and the other Sh.3.5 million with a probability of 0.3.

Required:

(i) Construct a decision tree depicting the above information using the expected monetary value (EMV) criterion.

(ii) Advise on the best decision using the EMV criterion.

April 2022

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