Quantitative Methods 2015 November Knec Past Paper

SECTION A (32 marks)
Grower ALL the questions in this section in the spaces provided after each question.
I A supervisor in a factory recorded tlie following figures of lateness, in minutes, for 20 workers.

Construct a frequency distribution table for the above data, starting with the classes 0-2, 3-5 … (4 marks)
2. Outline three advantages of using observation method in the collection of data. (3 marks)
3 Distinguish between a diagpnul matrix and a scalar matrix, giving an example in each case, (4 marks)
4 A firm’s labour force is growing at the rate of 5 percent per annum. Currently the firm has 500 employees. Determine its expected labour force in live years’ time. (2 marks)
A farmer borrowed Ksh 560,000 from a bank, lie was required to repay the lean with simple interest for a period of 48 months. The repayment amount was Ksh 21,000 per month.
Determine the simple interest rate per annum. (4 marks)
6 The mean age of 15 teenagers an a self-awareness class was 19 years. On a du teenagers was absent, the rest gave their ages as follows; 21.19,20. 19, 18. 17.
18, 16.22,20, Determine the age of the absent teenager. (2 marks)
An investor preparing to purchase a business. estimated the profits in the first year to be as
Profits (Ksh.'(MM)’s)   Probability
500                                      0.15
400                                      0.15
100                                        0.7
Calculate the expected value of profits in the first year (2 marks)
8. Stale three rules followed when drawing a network diagram

9. The prices of a certain commodity for a period of four months are given as follows:
Month Price  Kshs.)
January               40
February              45
March                 60
April «               55
Using January as the base period, calculate the price index for each month <4 marks)
10. Outline four components of a time series.

II, (a) Explain lour circumstances under which a researcher may prefer a sample to a census, in the collection of data, (H marks)
(b) 1 he distribution of profits uf SO companies are shown in the table below;

Calculate the:
(i) arithmetic mean
fii) variance.
(9 marks)
Sum her of l’i m putties

12. (a) Ina survey of 200 clients of an insurance company, it was found (hat:
90 had a life insurance policy
70 had a medical policy
7b had an educational policy
36 had life and education policies
30 had life and medical policies
40 had education and medical policies
N had life, education and medical policies
(i) Present the information above in form of a Venn diagram; di i Determine the number of clients who had:
I exactly one policy
II at least two policies
III none of the three policies.

13. (a) A firm has analysed (heir operating conditions and has developed the following functions:
Revenue • (TR) = 4U0Q – 4Q:
Cost (TC) Q:
+ 10Q ■ 30
Where Q is the number of units sold.
Determine the:
(i I Level of output (Q) that the Finn should sell in order to maximize profit,
(ii) Price that maximize profit;
(iii) Maximum profit (9 marks)
lb) Explain the meaning of each of the following terms as used in Financial Mathematics
(i) compounding
(ii) discounting
(iii) perpetuities
(iv) annuities.

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