**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. 20.18.21.17.

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

follows;

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.