### TUESDAY: 22 August 2023. Morning Paper. Time Allowed: 3 hours.

### Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings. Do NOT write anything on this paper.

**QUESTION ONE**

1. In relation to statistics, explain the following methods of collecting primary data:

Observation. (2 marks)

Questionnaire. (2 marks)

Interview. (2 marks)

2. Explain FOUR qualities of a good sample. (4 marks)

3. An importer based in Kenya imported 50 bales of clothes from Japan at a cost of 450 Japanese Yen (¥) per bale. He also incurred 100,000 Kenyan shillings (Kes) on freight charges, 2% insurance in transit charge on the cost of each bale and also paid Kes 1,000 per bale as customs duty.

At the time of importation, the prevailing exchange rate was 1 ¥ = 128 kes.

**Required:**

Compute the selling price per bale in Kenya shillings if the importer intends to make a profit margin of 25%. (6 marks)

4. The profit function of ABC Ltd. is given as:

**Required:**

Calculate the maximum profit of ABC Ltd. (4 marks)

**(Total: 20 marks)**

**QUESTION TWO**

1. In relation to data collection, distinguish between “open ended questions” and “closed ended questions”. (4 marks)

2. In an arithmetic progression, the sum of the first 20 terms is 400. The 8th term is three times the third term.

**Required**:

Calculate:

The 1st term of the series. (4 marks)

The common difference in the series. (2 marks)

3. A manufacturing company uses three machines in its production process; machine X, machine Y and machine Z. 30%, 25% and 45% of the total monthly production is produced by machine Y, machine X and machine Z respectively. Past production records indicate that out of the total production by machine X, machine Y and machine Z, 5%, 3% and 4% respectively of items produced are found to be defective.

**Required:**

Draw a probability tree for the above events showing the joint probabilities of a machine producing either defective or non-defective items. (5 marks)

The probability that the defective item was from machine X. (3 marks)

The probability that the defective unit was from machine Z. (2 marks)

**(Total: 20 marks)**

**QUESTION THREE**

1. Highlight TWO advantages and TWO disadvantages of geometric mean as used in statistics. (4 marks)

2. The following data shows the profits earned by 400 small and medium – sized enterprises (SMEs) in a country over a one-year period:

**Required:**

Compute the following:

The mean arithmetic profit for the SMEs. (4 marks)

The median profit for the SMEs. (4 marks)

The standard deviation of profit for the SMEs. (4 marks)

3. James Guyo deals in the sale of stationeries. In a given month, he sold 100 books and 250 pens for Sh. 22,500. In another month he sold 200 books and 360 pens for Sh. 40,800.

**Required:**

Using matrix algebra, calculate the unit selling price of a book and the unit selling price of a pen. (4 marks)

**(Total: 20 marks)**

**QUESTION FOUR**

1. Explain THREE applications of consumer price index (CPI). (6 marks)

2. A market researcher investigating consumer preference for three beverages namely; coffee, tea and chocolate in a given village collected the following data from a sample of 1,000 consumers:

300 consumed coffee.

290 consumed tea.

425 consumed chocolate.

50 consumed all the three beverages.

120 consumed coffee and chocolate.

150 consumed coffee only.

145 consumed chocolate only.

**Required:**

Present the above information in a Venn diagram. (4 marks)

Calculate the number of consumers who consumed tea only. (2 marks)

Compute the number of consumers who consumed coffee and tea but did not consume chocolate. (1 mark)

Compute the proportion of consumers who did not consume any of the three beverages. (2 marks)

3. A student bought a laptop computer on hire purchase terms. The marked price of the laptop was Sh. 42,500. The student paid a deposit of 25% of the marked price and the balance was to be paid in 18 months instalments of Sh. 2,750 per month.

A customer who buys the laptop computer on cash is given a discount of 5% on the marked price.

**Required**:

Compute:

The hire purchase price of the laptop computer. (3 marks)

The amount of money the student could have saved if he had bought the laptop computer on cash basis.

(2 marks)

**(Total: 20 marks)**

**QUESTION FIVE**

1. Enumerate THREE qualities of a good measure of dispersion. (3 marks)

2. Simplify the following algebraic expression:

3. Jacinta Moraa is an employee of Azed Company Limited. During the year 2022, her monthly income was as follows:

In the month of November 2022, her monthly income tax was Sh. 9,810.35 and her net pay was Sh. 50,917.50. Her personal relief was Sh. 2,400. She also enjoyed an insurance relief after taxation. The prevailing rate of tax during the year was as follows:

**Required:**

Calculate the gross tax charged on Jacinta Moraa’s monthly income. (3 marks)

Compute the amount of insurance relief that Ms. Moraa received in the month of November 2022. (2 marks)

4. Mbetan Muinde took a loan of Sh. 1,000 from a mobile money provider to be repaid in five (5) monthly equal instalments. The interest charged on the loan was 6% per month with the first payment being made after one month.

**Required:**

Calculate the monthly repayment amount. (3 marks)

With the aid of a table, analyse the payment of interest and the amortisation of the principal for the above loan. (6 marks)

**(Total: 20 marks)**