Question 1

1. (a)Distinguish between simple random sampling and stratified random sampling.
2. (2 marks)
3. (b)The following table shows the age range of employees at Abacus Ltd
4. Given that the modal age of the employees is 40 years;
5. Required:
6. (i)Determine the value of x . (8 marks)
7. (ii)Compute the harmonic mean age. (6 marks)
8. (iii)Represent the data given in the table above on a histogram.

Question 2

(a) Akello, a hotel proprietor in Ntinda Kampala, would like to build either a small hotel or a large hotel. Her plans will depend on the future demand the hotel will serve. She expects either hotel to succeed with a probability of 12. The profits expected from each type of hotel, per annum in million shillings, are shown in the following table.

Required:

Using expected monetary value criterion determine the:

1. (i)best type of hotel Akello should build.
2. (ii)redundant type of hotel Akello should abandon.

Age range

20 - 26

26 - 32

32 - 38

38 - 44

44 - 50

No of employees

5

12

x

20

14

Possible future demand

Type of hotel

Low

High

Large

200

270

Small

160

800

1. (b)A sample of 200 CPA students at KAMU College revealed that 18% of them were senior managers and a sample of 400 CPA students at High class College revealed that 15% of them were senior managers.
2. Required:
3. Determine whether there is a significant difference between the two proportions in the two colleges at 5% level.
4. (8 marks)
5. (c)The canteen at Tina Tana Nursery School sells ice cream packed in three differently shaped containers; cylindrical, conical and cuboid. The following data shows the shapes preferred by 60 children who buy the ice cream.
6. The null hypothesis states that there is no difference between the shapes preferred by the children.
7. Required:
8. Test at 5% level whether there is a significant difference between the shapes preferred by the children.
9. (ii)A random variable x has the Binomial distribution B(25, 0.38). Required:
10. Prove that the distribution can be approximated by a normal distribution.
11. (2 marks)
12. (iii)Use the normal approximation to binomial to calculate the probability that x takes on a value more than 15.
13. (3 marks)

Shape

No. of children

Cylindrical

17

Conical

24

Cuboid

19

Question 3

(a) (i)

Identify two conditions under which the binomial distribution B(n, p) can be approximated by a normal distribution.

(b) Two fair dice each with faces numbered 1, 2, 3, 4, 5, 6 are tossed together once and the sums of numbers appearing on top are recorded.

Required:

1. (i)Prepare possibility space for the sums.
2. (ii)Prepare probability distribution table for the sums.
3. (iii)Use the probability distribution to compute E( x ) for x 6.

(4 marks) (2 marks) (2 marks)

(c) At Nansana brick factory 10% of the bricks produced are found defective. A sample of 15 bricks was chosen at random from the factory.

Required:

Use the Poisson probability distribution to compute the probability that in the sample:

1. (i)exactly two bricks are defective.
2. (ii)more than one brick are defective.

Question 4

(a) Define the following terms.

1. (i)Marginal cost.
2. (ii)Index number.

1. (b)A farmer in Lwengo district, who is engaged in agri-business has established that his sales of coffee, y (in kilograms) depends on the
2. number of productive hours,x he dedicates to the business. The expression y (2x3 5)4 describes the relationship between y and x
3. Required:
4. Determine the rate at which the farmer's sales are changing given he dedicates 2 hours.

1. (c)Hambe car depot participated in a trade show to popularise a new model of a car in their warehouse. Hambe exhibited q cars and sold all of them.
2. The total cost function (in shillings) experienced by Hambe car depot for the exhibition is given byC2,000,0001,500,000q25,000q2 .
3. Required:
4. Determine the minimum cost of the exhibition. (5 marks)
5. (d)A real estate company based in Kampala collected the following data on average selling prices of three types of houses it sold in the past three
6. years.

Table 1: Average selling price (million shillings)

Table 2: Number of each type of house sold.

Required:

1. (i)Compute the un-weighted aggregate price index for the houses for 2015 using 2014 as the base year.
2. (2 marks)
3. (ii)Compute the Paasche price index for the 2015 and 2016 using 2014 as the base year.
4. (6 marks)
5. (iii)Comment on both indices obtained in (d) (i) and (d) (ii) above.