(Solved): ANSWER ALL QUESTIONS. SECTION A Use the information provided below to answer questions 1 to 6. As p ...

ANSWER ALL QUESTIONS. SECTION A Use the information provided below to answer questions 1 to 6. As part of a pilot study aimed at determining the daily consumption of water (in litres) across selected suburbs of Johannesburg, Johannesburg Water SOC Ltd (JW), a municipal entity, collected the sample data shown in Table 1 below. Cumulative frequency Class (1) 100 <150 150 < 200 200<250 250 < 300 300 < 350 350<400 Total Frequency, f Midpoint, 125 175 225 275 325 375 Max & 40 W 130 X 75 35 ?f fm 5 000 17 850 29 250 Y 24 375 13 125 ?fm Table 1: Daily consumption of water (in litres) Question 1 Determine the missing values represented by W. X. Y. and Z. A W=118; X = 102; Y = 35 450 and Z=6923 750 BW= 102; X=118; Y=32 450 and Z=8 923 750 C W=105; X=115; Y=32 450 and Z=8 923 750 D W=102, X=118; Y-37 450 and Z=6923 750 fm² 625 000 3 123 750 6581 250 Z 7921875 4921875 Question 2 Using the sample data in Table 1 above, determine the mean daily consumption of water. A 244.11 B 262.9 C 240.9 D 252.3L Question 3 Using the sample data in Table 1 above, determine the median daily consumption of water. A 243.1L B 241.5L C 247.9 D 238.3L 40 ? 272 ? [24 MARKS] 465 500 (4 marks) (4 marks) (4 marks) Question 4 Using the sample data in Table 1 above, determine the modal daily consumption of water. A 246.11 B 233.5 C 224.90 D 235.0L Question 5 Using the sample data in Table 1 above, determine the standard deviation of the daily consumption of water A 66.8L B 71.3 C 64.9L D 68.0 Question 6 Using the sample data in Table 1 above, determine the mid-80% range of the daily consumption of water. A 185.1L B 179.3L C 194.9 D 168.4L (4 marks) (4 marks) (4 marks) SECTION B Use the information provided below to answer questions 7 to 8. Fifteen percent of the products produced by an industrial robot are known to be defective. A quality-control inspector randomly selects 6 products from a production run. Question 7 [20 MARKS] (4 marks) What is the probability that at least two of the products selected by the quality-control inspector are defective? A 0.3772 B 0.7765 C 0.2235 D 0.3993 Question 11 (4 marks) Determine the probability that on a particular day, the restaurant generated revenues of exactly R11 699.16, R1 394.32 and R1 596.80 from the eat-in orders, take-out orders and the bar respectively. Assume that the three revenue sources are independent of each other. A 0.0298 B 0.0191 C 0.0064 D 0.8118 SECTION C Use the information provided below to answer questions 12 to 15. As part of the end-of-semester review of the marks obtained by third-year students in business statistics, the academic manager of Frontier Business School has captured the marks obtained by 10 randomly selected third-year students in their formative and summative assessments as shown below in Table 3. Student # Formative assessment 1 2 52 68 Summative assessment 58 66 Table 3: Marks obtained by 10 students in the formative and summative assessments The academic manager wants to determine whether students' performance (i.e., marks) in the formative assessment is a reliable predictor of students' performance (ie, marks) in the summative assessment. 3 91 81 A y= 25.707+0.9887x By=29.796 +0.5897x Cy=25.707+0.5897x Dy=29.796+0.9887x 4 74 70 Question 13 Determine the Pearson Correlation Coefficient. A 0.5897 B 0.8459 C 0.7155 D 0.9887 5 64 74 7 56 52 69 6 46 8 57 70 [16 MARKS] 9 10 83 62 83 60 Question 12 (4 marks) Which of the following is the equation of the relationship between the predictor variable (x) and the response variable (v)? (4 marks) Question 14 (4 marks) Using the simple linear regression equation, predict the marks obtained by a randomly selected third-year student in the business statistics summative assessment if the said student obtained a mark of 51 in the business statistics formative assessment. A 56 B 60 C 63 D 54 Question 15 (4 marks) The relationship between the independent variable (IV) and the dependent variable (DV) is likely to be mediated by a third variable (MV). With regard to the statement above, which of the following is most likely to be correct? A IV = Students' performance (.e., marks) in the formative assessment; DV=Students' performance (i.e., marks) in the summative assessment, and MV = Students' level of comfort with the venue of the assessments. B IV = Students' performance (.e., marks) in the summative assessment: DV= Students' performance (.e., marks) in the formative assessment, and MV = Students' level of preparation for the assessments. C IV = Students' performance (i.e., marks) in the formative assessment; DV = Students' performance (i.e., marks) in the summative assessment, and MV = Students' level of preparation for the assessments. DIV = Students' performance (.e., marks) in the summative assessment: DV = Students' performance (i.e., marks) in the formative assessment, and MV = Students' level of comfort with the venue of the assessments. SECTION D Use the information provided below to answer questions 16 to 20. A business analyst has obtained the following information (Table 4) on the prices (in Rands) and quantities (in boxes) of three flavours of ice-cream sold by a small business owner during 2016 and 2021. 2016 Price (Rands per box) Ice-cream flavours Vanilla Chocolate Strawberry Table 4: Prices and quantities of three different flavours of ice-cream. Quantity (boxes) 130 140 145 44 000 21 500 15 900 Price (Rands per box) 170 200 220 [20 MARKS] 2021 Quantity (boxes) 92 000 40 200 36 600 Question 16 Using 2016 as the base year, calculate the Laspeyre's Price Index for 2021. A 135.60 B 66.73 C 138.44 D 149.86 Question 17 Using 2016 as the base year, calculate the Paasche's Quantity Index for 2021. A 287.54 B 48.15 C 72.15 D 207.70 Question 18 Using 2016 as the base year, calculate the Pasche's Price Index for 2021. A 149.86 B 138.60 C 207.70 D 66.73 Question 19 Using 2016 as the base year, calculate the Laspeyre's Quantity Index for 2021. A 138.60 B 207.47 C 72.15 D 149.86 (4 marks) (4 marks) (4 marks) (4 marks) Use the information provided below to answer questions 23 to 25. The projected annual net cash flows associated with an investment opportunity are shown below in Table 5. The expected rate of return on the investment is 12%. Year Future Cash flows 1 220 000 2 250 000 3 300 000 4 200 000 5 180 000 Table 5: Annual net cash flows of the investment opportunity. Question 23 Discount factor Question 24 K 0.7972 M 0.6355 0.5674 Determine the missing values represented by K, L, M, and N in Table 5. A K = 0.8929, L = R196 438; M = 0.7118 and N = R213 540 BK = 0.9009; L = R198 198; M = 0.7312 and N = R219 360 C K=0.9174; L=R201 828; M = 0.7722 and N = R231 660 D K = 0.8929; L = R196 438; M = 0.7722 and N = R231 540 Calculate the total present value of the net cash flows from the investment opportunity. A R859 028 B R902 575 C R838 510 D R866 704 Present Values L 199 300 N 127 100 102 132 Question 25 If the Net Present Value of the investment opportunity is an unfavourable R11 490, what is the initial outlay? A R811 490 B R850 000 C R848 510 D R860 000 END OF PAPER (4 marks) (4 marks) (4 marks)