KASNEB Quantitative Analysis - Question 1b

Outline three assumptions of the transportation model. ... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 3c

The following data were obtained from the records of a certain company, relating to the year 2018: MonthTotal overhead costs - Y (Sh.)Direct labour hours - X... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 4a

The data below represent the number of students enrolled in a certain college over a four year period: Number of students enrolled QuarterYear123420157... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 5b

The manager of a certain project has identified the following information relating to the project: ActivityImmediate predecessor (s)Duration (weeks)Probabili... [Click to view full question and step-by-step solution]

November 2018

1a

Decision Theory

Explain the following terms as used in decision theory:

(i) Opportunity loss.

(ii) Expected value of perfect information.

1b

Linear programming

Outline three assumptions of the transportation model.

1c

Hypothesis Testing and Estimation

A company operates under two departments, P and Q. Details relating to a sample of employees working in the two departments has been provided as follows:

	Department P	Department Q
Number of employees	29	24
Average monthly salary	Sh.260,000	Sh.310,000
Standard deviation	Sh.25,000	Sh.30,000

Required:

Determine whether there is any significant difference between the average monthly salaries of employees working in the two departments. (Use a significance level of 5 per cent).

1d

Probability

Bidii College offers three courses namely; Accounting, Computing and Driving. The college has a total population of 500 students. Data obtained from the college revealed the following:

329 Students were undertaking Accounting course.

186 Students were undertaking Computing course.

295 Students were undertaking Driving course.

83 Students were undertaking both Accounting and Computing courses.

217 Students were undertaking both Accounting and Driving courses.

63 Students were undertaking both Computing and Driving courses.

Required:

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

(ii) The number of students undertaking all the three courses.

(iii) The number of students undertaking only one course.

2a

Mathematical Techniques - Calculus

ABC Limited manufactures and sells electronic calculators whose marginal cost function is given by:

MC = x - 100 (in thousands of shillings)

Where: MC is the marginal cost function.

X is the number of electronic calculators produced and sold.

The fixed cost of production amounts to Sh.250,000. The total revenue function is estimated to be quadratic in nature.

The table below shows the sales revenue realised by the company at three different production levels:

Number of electronic calculators produced and sold (x)	Sales revenue (Sh."000")
20	1,600
40	3,200
60	4,800

Required:

(i) The total profit function.

(ii) The maximum profit.

2b

Decision Theory

X Limited, Y Limited and Z Limited deal in the production of detergents. On 1 January 2017, the three companies introduced a similar new detergent in the market. Prior to introduction of the new detergent, the three companies had an equal share of the market. A survey conducted on the market shares of the three companies as at 31 December 2017 revealed the following:

X Limited had retained 90 per cent of its customers but had lost 3 per cent and 7 per cent of its customers to Y Limited and Z Limited respectively.
Y Limited had retained 75 per cent of its customers but had lost 10 per cent and 15 per cent of its customers to X Limited and Z limited respectively.
Z Limited had retained 80 per cent of its customers but had lost 5 per cent and 15 per cent of customers to X Limited and Y Limited respectively. its
There were no significant changes in the buying habits of the customers during the year.

Required:

(i) The market shares ofthe three companies as at 31 December 2018.

(ii) The long run market shares of the three companies.

3a

Hypothesis Testing and Estimation

Explain the following terms as used in hypothesis testing:

(i) Level of significance.

(ii) Region of rejection.

3b

Correlation Analysis

Summarise three factors that determine the size of the Pearson product moment correlation coefficient.

3c

Regression Analysis

The following data were obtained from the records of a certain company, relating to the year 2018:

Month	Total overhead costs - Y (Sh.)	Direct labour hours - X
January	14,250	856
February	13,000	536
March	13,000	640
April	12,500	600
May	13,250	680
June	13,750	808

Required:

(i) The least squares regression function relating the direct labour hours to the total overhead cost.

(ii) The coefficient of determination.

(iii) Comment on the results obtained in (c) (ii) above.

4a

Time series

The data below represent the number of students enrolled in a certain college over a four year period:

Number of students enrolled Quarter
Year	1	2	3	4
2015	70	100	80	60
2016	50	40	120	80
2017	60	70	70	40
2018	90	100	130	-

Required:

(a) The adjusted seasonal component for each of the four quarters, using the multiplicative model.

(b) Estimate the enrollment of students in each of the four quarters of year 2019 using the simple least squares method.

4b

Time series

Estimate the enrollment of students in each of the four quarters of year 2019 using the simple least squares method.

5a

Probability

Explain the following terms as used in probability theory:

(i) Mutually exclusive events.

(ii) Independent events.

(iii) Joint probability.

(iv) Conditional probability.

5b

Decision Theory

The manager of a certain project has identified the following information relating to the project:

Activity	Immediate predecessor (s)	Duration (weeks)	Probability
A	-	3 4 5	0.25 0.50 0.25
B	-	4 5 6 7 8	0.15 0.30 0.20 0.20 0.15
C	A	1 3 5	0.20 0.65 0.15
D	B,C	4 5	0.80 0.20
E	D	3 4 5 6	0.15 0.25 0.25 0.35
F	D	5 7	0.20 0.80
G	E,F	2 3	0.50 0.50

Required:

(i) A network diagram for the project.

(ii) The expected duration of the project.

(iii) Simulate the durations of the project on the basis of two runs.

November 2018

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