Question 2 (a) During a music festival, a group of 150 students did their rehearsals in committee rooms marked A, B and C respectively. Only students in rehearsals were allowed in the rooms. 90 students rehearsed in room A, 50 students rehearsed in room B, 70 students rehearsed in room C, 15 students rehearsed in both rooms A and C, 12 students rehearsed in both rooms B and C and 10 students rehearsed in all the rooms. Required: (i) Show the above information on a Venn diagram. (4 marks) (ii) Determine the number of students who rehearsed in both rooms A and B. (b) Given quadratic equation 2x2 ? 8x ? 8 ? c . Required: Find the value of x for which c ? 32 . (c) Kabalisa is a casual sales girl and she is paid a weekly wage of Shs 60,000 and a commission of 5% on goods sold above Shs 200,000 each week. In a certain week she earned Shs 130, 000. Required Determine the total sales of the goods she made that week. (6 Marks) (Total 20 marks) Question 3 (a) Define the terms: (i) sinking fund and identify one application of a sinking fund. (2 marks) (ii) Mark up. (1 mark) (b) A retailer bought his goods at a unit cost of Shs 150,000. In order to encourage his clients to purchase in large quantities he set his mark up to include tax and profit of 12%. Required: Determine the unit selling price of the retailer. (3 marks)

(c) A welding machine costing Shs 3 million is established to depreciate at a rate of 15% per annum. A metal fabricating workshop acquires this machine so as to improve their efficiency in meeting the client's expectations at the beginning of the year. Required: Using the reducing balance method find the: (i) depreciated value of the welding machine after 6 years. (ii) rate of depreciation that would depreciate the machine to Shs 2 million after 6 years. (4 marks) (c) Ms Nyaketcho Paula, a business woman borrowed Shs 15 million at a compound interest of 12% per annum. The loan is to be discharged at the end of the 3 years with regular six monthly payments into the sinking fund at a rate of 8% per annum,

Required:

Calculate the value of each installment Ms Nyaketcho pays to the sinking fund. (7 marks)

Question 4 (a) Explain four methods used in primary data collection. (4 marks) (b) The following are the grade point average (GPAs) obtained by seven different students at a University: 3.2, 4.5, 3.8, 4.0, 3.5, 3.2, and 4.1.

Required

Determine the median grade point average. (2 marks) (c) The management of an organization holds daily staff briefings meetings. The following data show the time (in minutes) spent on a sample of 25 briefings. 28 21 19 35 23 31 37 31 16 33 25 32 32 42 29 26 41 43 23 28 48 25 26 38 36

Required: (i) Construct a frequency distribution of equal class widths starting with class 15 - 19. (2 marks) (ii) Hence calculate the mean. (4 marks) (iii) Calculate the lower quartile. (3 marks) (iv) Draw a histogram from the frequency distribution and the estimate the mode.

Question 5 (a) Distinguish between dispersion and skewness in statistical data analysis. (2 marks) (b) The temperature in degrees centigrade of 12 patients in a referral hospital was measured and the results were recorded as follows: 38.0 37.7 37.8 38.6 37.0 36.8 37.4 38.8 38.7 37.8 37.9 37.5 Required: Determine the: (i) temperature range of the patients. (ii) The standard deviation. (iii) Comment on the temperature variation (c) A production function of a firm that makes juice is given by P(x) ? (2x ? 4)3 (3x ? 2)2 . Required: Using an appropriate method, find the rate of change of production of the firm. (6 marks)

Question 6 (a) (b) (i) With an example, define the term mutually exclusive events. (2 marks) (ii) Using a Venn diagram illustrate mutually exclusive events L and D in a sample space S. (2 marks) Lartex investment Ltd manufactures packaging materials. In order to guide the production department on how to meet their daily targets and sell q cartons of the packaging materials, the financial controller (c) A board of directors in a certain private organization comprises of 7 members of whom 5 are female and 2 are male. The organization is to be represented in the annual general meeting by 3 board directors. Required: Determine the number of ways of selecting the 3 board directors to attend the annual general meeting if; generated a cost function C(q) ? 5000q ? 4000 P(q)?2000q?4q2 ?4000. Required: Determine the: (i) revenue function, R(q) (ii) production that maximizes revenue. and a profit function (3 marks) (5 marks) (i) any of the directors can be selected. (ii) the two males directors must be selected (iii) at least one female director is to be selected

FORMULAE Combination "C, =- n! (n-r)!r! n! 2 Permutations " p, =- (n-r)! 3. Harmonic mean (ungrouped data) hm = " 4 . Harmonic mean (grouped data) hm = - n 5 . Mean, x = A+ E fd Efx Es or Mean, x = Ef Geometric mean = V(1+p,)(1+P12)....(1+p.) V(1+p,)(1+P12).....(1+P,.) 6. Where p is the proportional increase. N - Cfb 7. Median = Lb+ 2 C fm 8. Mode = Im + d , d , + d 2 ) C 9. Variance Var(x) = 6 = VES 10. Sample standard deviation or E(x-F)? S= n-1 11. Standard deviation S=. E.fd V Ef Ef 12. Pearson coefficient of skewness Sk = (x -mode) 3 x- median or Sa Sk = Sa 13. Price relatives = P x 100 Po