Question 1 (a) Distinguish between: (i) Systematic sampling and multi-stage sampling techniques. (2 marks) (ii) Population mean and sample mean. (2 marks) (b) To cross Burkina Faso border post, a tourist is required to present his/ her bank statements showing his/ her account balance (in US dollars). The following table shows the distribution of the account balances for a sample of 92 tourists in December 2018. Account balance No. of tourists The Customs manager at the border would like to get this data further analysed for management use, Required: (i) Calculate Bowley's coefficient of skewness for the above data. (9 marks) (ii) Construct a Lorenz curve representing the account balances of the tourists. (7 marks)

Question 2 (a) Akandi Drinks Ltd, a soft drinks company based in Kampala needs to appoint managers for each of their four substations in Jinja, Lira, Entebbe and Ishaka respectively. Four women and six men are available for appointment. Required: Determine the: (i) possible number of appointments that can be made in order to have an equal number of men and women appointed. (3 marks) (ii) probability of appointing two other managers if one man and one woman were already in acting managerial positions and awaiting confirmation. (3 marks) (b) The data below shows the minutes by which 30 trainees at Kamwe Kamwe hardware were late in their 2 months of internship. Required: (i) Construct a frequency distribution table for the data above with classes of uniform class interval size starting from 0 - 9. (2 marks) (ii) Compute the unbiased estimate of the mean time. (4 marks) (c) The mass of goats in Mbale and Arua is normally distributed with a standard deviation of 4 kg and 9 kg respectively. A random sample of 50 goats from Mbale had a mean mass of 30.3 kg while 40 goats from Arua had a mean mass of 30 kg. Required: (i) Test the hypothesis at 1% level that goats in the two districts are of equal mass. (6 marks) (ii) Comment on the result in (c) (i) above. (2 marks) Question 3 (a) Distinguish between: (i) Correlation and causation as used in correlation. (2 marks) (ii) Simple linear regression and multiple linear regression. (2 marks) (b) Smart Motors are testing the braking system of a new car model. The table below shows the braking distance Y (km) for different speeds X kmh-1. Speed ( X ) 30 Required: (i) Use the least squares method to calculate the equation of the trend line in the form Y a bX . (9 marks) (ii) Use the equation of the trend above to estimate the braking distance of a car travelling at a speed of 55 kmh-1. (1 mark) (c) The table below shows quantities and prices of different types of car tyres sold by an agent in the months of January and July 2018. January July Type of tyre Quantity Price Shs '000' Quantity Price Shs '000' Linglong Required: Given that the Paasche's quantity index was calculated as 110; determine the price of Savero GT in July using January as the base period. (6 marks)

Question 4 (a) Explain the term 'marginal cost'. (2 marks) (b) JJ Metal Factory Ltd fabricates iron rods for sale. Their total daily revenue is given by the function 2 R(q) 50 2q 2q 2 ; where q is the number of iron rods sold. Required: (i) Determine the number of sales that will maximise total revenue. (11 marks) (ii) Calculate the maximum total daily revenue earned. (2 marks) (c) Agnes and Jane went to Mutundwe market to buy rice and beans. Agnes paid a total of Shs 415,000 for 35 kg of rice and 61 kg of beans while Jane paid a total of Shs 347,500 for 28 kg of rice and 55 kg of beans. Required: Compute the unit price for each commodity. (5 marks) (Total 20 marks) Question 5 (a) Explain any four assumptions of linear programming. (4 marks) (b) Opolot deals in secondhand cars of two types, Toyota Hiace TH and Nissan Caravan NC. He has Shs 800 million to invest in an inland car depot that accommodates 26 cars. TH costs Shs 40 million while NC costs Shs 25 million. The expected profit on TH is Shs 2 million while on a NC is Shs 1 million. Required: (i) Express the above information as a linear programming model. (4 marks) (ii) Using the graphical method, determine the number of cars that Opolot should stock in order to maximise profits. (6 marks)

(c) The monthly expenditure on salaries and wages (in million shillings) of a science based University in Nansana in 2018 is as shown in the table below. Month Shs ,million' January 355 February 380 March 420 April 400 May 410 June 450 July 430 August 440 September 480 October 460 November 500 December 540 Required: (i) Calculate the three monthly moving averages of the expenditure. (2 marks) (ii) Illustrate the expenditure and the moving averages graphically. (3 marks) (iii) Comment on the trend. (1 mark) (Total 20 marks) Question 6 (a) Define the following terms in project network analysis. (i) 'Float'. (1 mark) (ii) 'Cost slope'. (1 mark) (b) A local council has identified project activities, time and resources to develop the community .The project has the following time and resource data.

Required: (i) Draw a Gantt chart for the project activities. (7 marks) (ii) Determine the critical path of the project. (3 marks) (c) Hakim Messi a fresh graduate has to make a choice between opening up a hardware shop and starting an agricultural mixed farm. There is a proposal to amend the tax laws for the two business ventures. If the laws are maintained, the expected turnover from the hardware shop and the mixed farm is 9 million and 14.5 million respectively while if the laws are amended, the expected turnover for the hardware shop and mixed farm will be 6 million and 8 million respectively. Statistics from research indicate a 70% chance that the laws will be maintained. Required: (i) Construct a decision tree for the information above. (3 marks) (ii) Using the expected monetary value criteria, advise Messi on which choice to make.