Calculate the mean speed in miles per hour attained between zero (0) and seven (7) for this distribution. (4 marks) A. 56.73 B. 75.63 C. 73.56 D. 76.05 2. Calculate the variance for the distribution given in Figure 1. (4 marks) A. 429.84 B. 492.98 C. 924.86 D. 942.99 3. Calculate the standard deviation and the co-efficient of variation respectively for the distribution given in Figure 1. (4 marks) A. 73.20, 28.20 B. 20.73, 0.28 C. 27.30, 20.28 D. 0.28, 0.2110. Further to the information provided in question nine (9) above, we are informed that nails produced that are shorter than the minimum acceptable length have to be scrapped. Consider that 4.8cm is still the minimum threshold for acceptable nail length. If the cost to produce one nail is 45 cents, how much does the company incur in Rand losses due to scrapping? (4 marks) A. R247.70 B. R347.91 C. R237.60 D. R471.99 11. Further considering information given in questions nine (9) and ten (10), if no more than 2% of nails are to be scrapped, what should the new mean be set at in millimeters? Assume that the standard deviation remains unchanged. (4 marks) A. 51.28 B. 52.21 C. 68.92 D. 69.28 12. Statistics show that only 25% of South African taxpayers submit their tax returns before the deadline date. Given a sample of six South African adults, what is the probability that exactly three have submitted their tax returns before the deadline date? (4 marks) A. 0.132 B. 0.453 C. 0.853 D. 0.343 13. Consider this question stem for this current question [13] and the next question [14]. Statistics show that 40% of men renew their car licenses after the deadline date. Assume that this statistic is true and consider seven randomly selected men. Determine the probability that exactly 3 men renew their car licenses after the deadline date. (4 marks) A. 0.39 B. 0.41 C. 0.29 D. 0.3114. Consider the question stem given in question [13] and calculate the probability that at most five men renew their car licenses after the deadline date. (4 marks) A. 0.96 B. 0.69 C. 0.98 D. 0.02 15. The duration of flights between two locations is normally distributed with a mean of 6 hours and a standard deviation of 45 minutes. Approximately what percentage of these flights can be expected to take between 7 and 8 hours? (4 marks) A. 0.088 B. 0.098 C. 0.988 D. 0.889 16. A survey by the National Retail Federation found that women spend on average R146.21 on a Saturday lunch. Assume the standard deviation is R29.44. Find the percentage of women who spend less than R160.00 on a Saturday lunch. Assume the variable is normally distributed. (4 marks) A. 0.69 B. 0.59 C. 0.68 D. 0.95 17. A survey by the National Retail Federation found that women spend on average R146.on a Saturday lunch. Assume the standard deviation is R29.44. Find the percentage of women who spend less than R190.00 on a Saturday lunch. Assume the variable is normally distributed. (4 marks) A. 0.88 B. 0.74 C. 0.93 D. 0.8218. Use the information in Figure 2 below to answer questions 18 through to 22. The data in Figure 2 below has to do with the stocks of three of South Africa's biggest mobile network operators STOCK PRICE QTY PRICE QTY Poqo Poqi P190 Po go P1 91 2008 2008 2011 2011 MTN 285 370 215 480 Vodacom 155 320 120 380 Cell C 110 700 90 800 Figure 2 Calculate the approximate price relatives to two decimal places for the MTN and Vodacom stocks over the period in question. (4 marks) A. 0.71, 0.67 B. 0.57, 0.75 C. 0.75, 0.77 D. 0.70, 0.81 19. Calculate the approximate quantity relatives to two decimal places for the MTN and Cell C stocks over the period in question. (4 marks) A. 3.01, 1.41 B. 1.03, 4.11 C. 1.30, 1.14 D. 0.03, 4.00 20. Looking at the stock information in figure 2, what would you conclude about the South African Mobile Phone sector between 2008 and 2011? (4 marks) A. The market was very depressed between the period 2008-2011 as cellular stocks remained below 2008 prices through the period to 2011. B. The market was solid and prices were rising between 2008 and 2011 C. Prices fell steadily but investors remained hopeful that the market was going to rebound in the near to medium term D. The market crashed and plateaued between 2008 and 201121. Calculate approximately to 3 decimal places the composite price index for all three stock between 2008 and 2011. (4 marks) A. 1.24 B. 0.88 C. 0.780 D. 1.42 22. Calculate approximately to 3 decimal places the composite quantity index for all three stocks for the period 2008 to 2011. (4 marks) A. 1.322 B. 1.323 C. 1.223 D. 1.232 23. The numbers of tourists (in thousands) visiting Table Mountain in Cape Town per quarter, for three consecutive years from 2036 to 2038 are presented in Figure 2 below: QUARTERS [X] SALES [Y] X2 Y2 XY 195 2 216 3 232 300 5 158 6 228 183 298 9 180 10 198 11 200 12 307 Ex = 78 Ey = A Ex = B Ey= = C xy = D Figure 2Compute the actual values indicated by A, B, C and D in that order. (4 marks) A. 2569, 560, 996553, 87103 B. 996553, 2569, 87103, 560 C. 650, 632699, 18730, 9562 D. 2695, 650, 633599, 17830 24. If the general linear regression model is given by the equation: y = a + bx; considering the information obtained in Figure 2 above, compute the value of b. (4 marks) A. 210.185 B. 121.852 C. 21.850 D. 2.185 25. If the general linear regression model is given by the equation: y = a + bx; considering the information obtained in Figure 2 above, compute the value of a. (4 marks) A. 397.210 B. 973.102 C. 210.379 D. 237.0214. The mean of a set of eight numbers is 10. If one of the numbers is removed the mean of the remaining numbers is 9. The number that was removed is: (4 marks) A. 16 B. 17 C. 15 D. 18 5. Consider the following frequency distribution of x-values: (4 marks) x: 5 10 20 25 f: 3 7 8 2 The mean of these data values is: A. 15.00 B. 14.75 C. 14.50 D. None of the above6. The following histogram gives the times taken by a random sample of workers of a company to complete a specific task. ONWAGONOS Number of Workers 10 20 40 50 60 70 80 90 Time (min) An estimate of the mean time taken by this group of workers is: (4 marks) A. 51.7 min B. 47.0 min C. 49.7 min D. 50.0 min7. Consider this question stem for both the current question (7) and question eight (8): A sample of ten employees at an auditing firm is randomly selected. The probability that three employees in this sample have an honors' degree is 0.215 while the probability that four employees in this sample have an honors' degree is 0.251. Given that the probability of a success is p, determine the value of p approximate to three (3) decimal places. (4 marks) A. 0.084 B. 0.400 C. 0.854 D. 0.454 8. Using the information in question seven (7) and the result obtained thereby, determine the probability that at least two employees in this sample have an honors' degree. (4 marks) A. 0.549 B. 0.228 C. 0.495 D. 0.954 9. A company producing steel nails receives an order for 5000 nails of length 50 mm. Due to external factors such as temperature and pressure, the lengths of the nails produced by the machine is normally distributed with a standard deviation of 1.6 mm. Acceptable lengths (lengths that any customer will consent to buy) must have a tolerance of 2 mm. If the machine is set to produce nails with a mean length of 5.0 cm, determine the percentage of nails that are acceptable. (4 marks) A. 0.7888 B. 0.8877 C. 0.9921 D. 0.78781. You are given a Grouped Frequency Distribution Table of the speed in miles per hour (mph) attained by each observed Formula One driver from zero (0) to seven (7) seconds, during the first practice session in preparation for the Abu Dhabi Grand Prix of 2022 as shown in Figure 1 below: Interval Frequency Cumulative Midpoint X2 fX fX2 [f] Frequency [X] 30