Question 1 (a) (i) Distinguish between discrete and continuous data. (2 marks)

(ii) Explain the advantages of grouping data. (2 marks) (b) The daily hours of sunshine in Kampala from 1st August 2020 to 9th September 2020 from the metrological department in Entebbe were as shown below: 7.0 7.6 12.5 12.9 8.3 9.7 8.3 11.1 7.5 8.1 7.5 9.8 10.4 11.6 11.3 7.3 7.8 6.5 6.2 8.4 6.1 5.6 5.6 5.8 4.8 4.3 3.0 2.6 2.8 3.9 2.6 3.2 2.4 2.6 9.2 7.3 7.0 6.5 10.1 5.5 A district Agricultural officer was interested in advising the farmers about the weather conditions that favour drying of their produce.

Required: (i) Using uniform class intervals and starting with the class 2.0 - 2.9; construct a frequency distribution table for the data above. (3 marks) From the table above, calculate the following: (ii) Average number of hours of sunshine per day. (2 marks) (iii) Co-efficient of variation and comment on the result. (6 marks) (c) ALD a non-governmental organization has carried out a research on the age distribution for teachers in school A and school B in the newly created district of Mbikwe in Eastern Uganda. The results are as shown in the table below. Age 20- 25- 30- 35- 40- 45- 50- 55- 60- Frequencies School A School B 4 0 6 2 11 4 14 7 9 11 5 12 5 11 3 8 0 5 16 March, 2021

Required: (i) Draw frequency polygons on the same graph to compare the age distributions of the teachers in school A and B. (4 marks) (1 mark) (Total 20 marks) (a) Explain the characteristics of a binomial distribution. (b) CICL LTD has recently opened a chocolate company in Namanve industrial park. Due to inexperience of the newly recruited staff, 10% of the chocolates produced in the factory are mis-shaped. In a sample of 1000 chocolates, find the probability that the number of mis-shapes is: (i) Less than 80. (2 marks) (ii) Between 90 and 115 inclusive. (3 marks) (c) The manager of VHL has established that the number of customers visiting his office follows a discrete random variable r with probability P(r) defined by P(r)?kr2 r=1,2,3 P(r)=k (7?r)2, r=4,5,6 P(r) = 0, otherwise

Required: Determine; (i) The value of k (ii) The mean number of customers that visit the manager's office. (4 marks) (d) NELN General Services Ltd a dealer in whole sale business receives customers at an average rate of 4 customers per minute. Assuming that customers' arrivals follow a Poisson distribution; Required: Calculate the probability that: (i) No customer arrives in any particular minute. (2 marks) (ii) Two or more customers arrive in any particular minute. (4 marks) (Total 20 marks) (ii) Comment on your results.

Question 3 Explain the following terms as applied in hypothesis testing. (i) Hypothesis (ii) Critical value (iii) Null hypothesis (1 mark) (1 mark) (1 mark) In a certain meeting, the guests were served with the breakfast of cereals with constituents A, B, C, and D. The cost of the cereals in Uganda shillings per kilogram in July, August 2020 and quantities needed were as shown in the table below. ABCD July Prices (Shs) 800 1,050 1,200 800 Quantities(kg) 6 4 3 2 August (c) Prices (Shs) 880 1,260 1,500 1,080 Quantities(kg) 8 5 2 3

Required: Using July as the base month: (i) Calculate the simple aggregate price index for August 2020. (2 marks) (ii) Compute Laspreyres quantity index for August 2020 and comment on the result. (4 marks) Kalilo Farmers Association deals in the growing and production of maize, they need to insure their produce against the unexpected weather patterns. The last released information from national forecasters show that the probability of receiving rain in the next six months is 0.75. They can decide to insure their produce in order to attract investors or fail to insure such that they sell on the local market. Using past records, their sales during a rainy season fetch 10 million if insured otherwise 8 million. If there is no rain, the sales fetch 9 million if insured otherwise only 6 million as shown below: Decision alternatives Insure Not Insure states of nature Rain No Rain 10,000,000 9,000,000 8,000,000 6,000,000 16 March, 2021

Required: Demonstrate if the farmers should insure their produce? (5 marks)

(c) The personnel manager of a large firm is investigating whether there is any association between the length of service of the employees and the type of training they receive. A random sample of 200 employee records is taken from the last few years and is classified according to these criteria. Length of service is classified as short; (less than one year), medium (1- 3 years) and long (more than 3 years) type of training is classified as being merely an initial induction, on job and continuous training. The data is as follows. Type of training Required: Induction Course On job &continuous Length of service short medium long 26 30 24 28 32 60 Question 4 (a) Explain the applications of linear regression. (3 marks) The Manager of a certain office supervises 10 clerical assistants, each using the word-processor. The assistants did not receive the same training in the use of word-processor. In order to make an assessment of the need for training, the manager monitored their work during a given week recording the number of pieces of work correctly produced (x)and the number of days spent on training ( y) . The results are summarised in the table below. x 35 26 33 22 40 31 22 20 24 23 y

Required: (i) Determine the equation x on y by least squares method. (8 marks) (ii) Using the equation, find the number of pieces of work produced correctly if a person is trained for 14 days. (1 mark) Using Chi - square, examine at the 5% level of significance whether this data provide evidence of association between length of service and type of training, stating clearly your null alternative hypothesis. 10 2 7 5 11 8 9 3 8 2

(c) ABC Ltd is the leading distributor of Yamaha motor cycles in Uganda and their sales as at November 2020 are as shown in the table below. Months Sales Jan 540 Feb 550 March 660 April 510 May 480 June 500 July 470 August 460 September 510 October 550 November 590 In 2020, the company recruited a new General Manager and he would wish to make forecasts based on the previous sales.

Required: Using smoothing constant a ? 0.2 and January sales as February forecasts, (i) Find the forecasted sales corresponding to the year 2021. Question 5 (a) XYZ is the leading distributor of Tampako drink. Their fixed costs are Shs 660 per unit. The variable costs are given by the functionV(x)?250?2x2, where x is the number of units produced per day.

Required: (i) Derive a function to determine the total costs for a day. (2 marks) (ii) Find the minimum costs per day. (4 marks) ABIB Ltd specialises in the production of hedges (x)and doors (y).The raw material absorption of the two products per day follows a production

FORMULAE 1 . Combination "C, =- n! (n-r)!r! 2. Permutations " p, =- n! (n-r)! 3. Mean of the binomial distribution = np 4. Standard deviation = Vnpq 5 . Variance of the binomial distribution = np(1 - p) 6. Standard error of population proportion Sp,, = Pq n 7. Spearman's rank correlation coefficient r = 1- 6Ed n(n - 1) Product moment coefficient of correlation = 8. 9. Cost slope crash cost - normal cost = normal time - crash time 10. Harmonic mean (ungrouped data) hm = n 11. Sample mean X = n 12. Harmonic mean (grouped data) hm = n 13. Quartile coefficient of dispersion = 93 -21 14. Bowley's coefficient of skeweness = 23 + 21 -202 15. Mean x = A+ _ fa or Mean x= MM(0) Required: (i) Sketch a graph of y=4x-2xz (8 marks) (ii) From the graph, find the maximum number of hedges and doors that can be produced in the above factory per day. (1 mark) A new car dealer in Namanve industrial park assembles two types of cars, Sanny and Hiace. On a certain day he assembled 4 Sanny and 2 Hiace at a total cost of Shs 80,000,000. The following day he assembled 3 San ny cars one Hiace at a total cost of Shs 50,000,000. Required: Using matrix method, find the total cost of assembling each car. (5 marks) (Total 20 marks) Question 6 (a) (b) Explain the following terms as applied in linear programming. (i) Dual (1 mark) (ii) Primal (1 mark) COMBO Ltd is a transport company specializing in the delivery of cement in the East African region. It has been doing all its operations using the manual system. During the recently concluded audit, the auditors advised the management to embrace application of technology in their operations. The managing Director hired a consultant from South Africa to develop for him a software that can help him manage his fleet well. The consultant has sent him a schedule of activities on a network as shown below