1. Which of the statements about Fischer’s method of computing index is/are  true?

2. The data below shows the weight and index numbers for six commodities in the state of Banana :

The weighted index number of the six commodities is 645.6 and the total weight is 300.
Required
a.The weight of commodity C
c.The index number of commodity E

3. The table below shows the year of study and the favorite s subject of 1,460 students of Pamoja University:

Required
If a student is randomly selected from this sample, determine the probability that:
a. The student’s favorite subject is math.
b. The student is in form one (1).
c. The student's favorite subject is English given that the student is in Form Two (2).
d. The student’s favorite subject is History or English given that the selected student is in form three (3).

4. TRUE or FALSE: Two events are independent of one another if the probability of the joint event is the product of the probabilities of the separate events, {i.e., if P (A ∩ B) = P (A)P (B)}.

5. In the year 2023, The East African Conference was attended by 570 delegates from Kenya, Uganda, and Tanzania (TZ).The following information relates to the delegates who attended the conference:

Required:
a. A Venn diagram to represent the above information.
b. The number of delegates not representing any of the three countries.
c. The number of guests that represented only one country.
d. The number of guests that represented two countries only.
e. The number of guests that represented at least two countries.

Moses is paid 12% interest in the first year,10% in the second year and 15% in the third year.
6. Required
The average rate of return of using geometric mean.

7. TRUE or FALSE: The harmonic mean is the appropriate mean if the data is comprised of rates.

8. ________sampling is a sampling methodology where data is collected from a homogeneous group.

9. Which of the following represents examples of secondary data collection methods?

10. (i)______is sales minus the cost of goods sold, while (ii)____ is the amount by which the cost of a product is increased in order to derive the selling price.

11. Mateso bought a Fridge set on hire purchase terms. The deposit was indicated as KES 70,000 and the balance payable in 12 equal installments of 9,000. As a policy of the company, a customer who defaults on an installment is charged a penalty of 10% on the outstanding balance payable in the next month. Mateso defaulted on the fifth month.

Required

The total cost of the Fridge bought by Mateso.

12. __________matrix refers to a square matrix in which all the off-diagonal elements are zero and all the on-diagonal elements are equal.

13. Tazama sells two(2) types of hats; Black and Red. The cost of producing 20 black hats and 16 red hats of KES 8,120. The cost of producing 8 black hats and 14 red hats is KES 5,680. Tazama makes a markup of 20% and 30% on queen cakes and black forest respectively.

Required:
a. Using matrix algebra, determine the cost of producing a black hat and a red hat.

b. The selling price of a black hat and a red hat.

14. The total manufacturing cost function of Lawingu Ltd is quadratic in nature and passes through the following points:

Required:
(a). The total manufacturing cost function.
(b). The total manufacturing cost incurred in producing 250 units of the product.

15. TRUE or FALSE: If Laspeyre's price index is 118 and Paasche's price index is 112, Dorbish-Bowley’s Price Index Number=1.05

16. Use the data below to calculate
a. Laspeyre’s index
b. Paasche’s index
c. Fisher’s index

17. Using the Venn diagram below, investigate whether A U(B∩C) equals (A ∪ B) ∩ C.

18. Mazuri College has 840 students whose participation in various sports as follows:

Required
a. A Venn diagram to represent the above information.
b. Number of students who played at least two of the sports.
c. Number of students who played one sport only.
d. Number of students who did not play any of the three sports.

19. TRUE or FALSE: The interest on KES 2,000 for six months at a 7.5% annual rate of interest is KES 150.

20. In a college student body election, there are four candidates: Amina, Baraza, Chale, and Daudi. Based on our polling analysis, it is estimated that Amina has a 20 percent chance of winning the election, Baraza has a 40 percent chance of winning, Chale 10 percent, and Daudi 5 percent. What is the probability that Amina or Baraza win the election?