(a) List three demerits of using interview as a method of data collection.

(3 marks)

(b) Iwarata Company Ltd deals in fruit export on behalf of farmer groups

producing fruits commercially in the Eastern district of Soroti. The

following table shows a record of their average weekly exports in metric

tonnes:

Weight Number of consignments

10-20 4

20-30 8

30-40 15

40-50 20

50-60 24

60-70 16

70-80 10

80-90 3

Required:

(i) Plot a Lorenz curve to represent the above data. (3 marks)

Compute the:

(ii) weekly mean weight. (3 marks)

(iii) modal weight. (3 marks)

(iv) Karl Pearson's coefficient of skewness given the standard deviation

as 16.6958 metric tonnes.

(2 marks)

(c) The statistics department in one of the universities conducted a survey of

income distribution among the business community in the neighbourhood.

The following data shows the results of the survey.

Capital (Shs million) 20-30 30-40 40-50 50-60 60-70 70-80

Frequency 18 26 40 30 16 10

Required:

(i) 80th percentile weight. (5 marks)

(ii) Outline the purpose of a Lorenz curve. (1 mark)

Question 2

(a) Explain the following terms as used in statistics:

(i) Point estimator (2 marks)

(ii) Confidence interval. (2 marks)

(b) A firm produces electric bulbs. A random sample of 1,000 bulbs has a

mean life for each bulb equal to 1,200 hours and standard deviation of 210

hours.

Required:

Calculate the 95% level of confidence for the population mean life of the

bulbs.

(4 marks)

(c) The table below shows pay-offs, in million shillings, for three activities X,

Y, Z and the states of nature P, Q and R.

Activity

State of nature (Pay-offs)

P Q R

X -120 200 260

Y 80 400 -260

Z 100 -300 600

Probability 0.3 0.5 0.2

Required:

(i) Construct a decision tree for the above data.

(4 marks)

(ii) Using the expected monetary value method, determine the best

course of action and justify your answer.

(8 marks)

(Total 20 marks)

Question 3

(a) (i) Describe the characteristics of a Poisson distribution. (4 marks)

(ii) An events management company has a number of wedding cars

which it hires out during the week. The daily demand for a car

follows a Poisson distribution with mean 3.5.

Required:

Compute the probability of days on which 2 cars were demanded.

(5 marks)

(b) A soft drinks factory based in Kawempe uses three lines K, Q, and R to

produce 45%, 30% and 25% of its total production respectively. The

percentage of sub-standard drinks from the three lines are 5%, 6% and

9% respectively. Given that a soft drink is selected at random;

Required:

using Bayes' theorem, compute the probability that the drink selected:

(i) is not sub-standard. (4 marks)

(ii) and found to be sub-standard was produced by line Q. (3 marks)

(c) A refugee agency is to choose 5 refugees, at random, from a group

containing 5 men, 3 women and 6 children, to be relocated to a less

congested camp.

Required:

Compute the probability that exactly 3 of those chosen will be men.

(4 marks)

(Total 20 marks)

Question 4

(a) Distinguish between marginal cost and marginal revenue. (2 marks)

(b) JL Apparels produces and sells school attires to various schools within

Kampala. The total cost function C for producing and marketing q units

of their products is given by 5 20 30,000 300,000 3 2 C q q q q .

Required:

(i) Find the total cost when the output is equal to 300 units.

(2 marks)

(ii) Find the marginal cost when the output is equal to 300 units.

(4 marks)

(c) The table below shows commodity prices (in Shs) and quantities (kg) in

two different years.

2014 2016

Commodity Price Quantity Price Quantity

Sorghum 5,200 100 6,000 150

Beans 4,000 80 5,000 100

Maize 2,500 60 5,000 72

Peas 12,000 30 9,000 33

Required:

Compute the price index numbers for 2016 taking 2014 as the base year

and comment on your results using:

(i) Laspeyre's method. (6 marks)

(ii) Paasche's method. (6 marks)

(Total 20 marks)

Question 5

(a) State the importance of correlation. (2 marks)

(b) Students at Summit Training Institute did mock examinations in Economics

and Quantitative Methods (QM) in preparation for the ICPAU June 2018

examinations and obtained the following scores:

Economics(x) 40 75 60 35 86 44 55 70 80 65

QM (y) 40 85 68 42 90 45 64 76 81 49

Required:

Using the Karl Pearson's method, compute the correlation coefficient

between scores in Economics and Quantitative Methods.

(10 marks)

(c) KK Bakery bakes cakes and bread. Each cake and loaf of bread earns a

profit of Shs 300 and Shs 400 respectively. To produce a unit product of

each, KK uses machine and labour hours as shown in the table below:

Machine (hours) Labour (hours)

Cake (x) 5 5

Loaf of bread (y) 3 7

Total available 101 181

Required:

(i) Construct a linear programming model for the above data.

(3 marks)

(ii) Determine the optimal solution using the simplex tableau method.

(5 marks)

Question 6

(a) Wotile factory located in Namanve manufactures high quality tiles. Its

average monthly output, in metric tonnes, of the various products in 2016

are given in the following table:

Month(x) January February March April May June July August

Output(y) 8.0 7.5 6.1 8.0 9.5 10 12 8.7

Required:

(i) Using the least squares method, determine the trend line of y on x

(y= a + bx).

(9 marks)

(ii) Using the trend line in (i) above, estimate the output of Wotile

factory in September 2016.

(1 mark)

(b) Kitiibwa Quirinos is the Supervising Engineer in KQ Engineering Consult

Ltd. The job at hand has been categorised into three stages. The first

stage of the job is to be handled according to the following precedence

schedule of activities