An entrepreneur plans to sell 10,000 anti-gravity hoverboard at a price of $s per board. It costs $m to manufacture each. [$s and $m are specified for each team.] She promises the customers that any failed unit will be replaced (only once) by a brand new unit within the warranty period. The entrepreneur needs to determine the warranty period that will ensure at least a 20% profit (calculate profit based on total expenses). You are asked to determine the maximum warranty period, in whole months, that she could afford to offer. A series of tests of 19 units (sampling) to estimate the Time-Of-Failure (TOF, in months) yields the data given in the attached document: 'shoesDATA'. The "red entries" in the data indicate aborted tests, meaning the tests were stopped before failure occurred. a) Using mean-ranking method fit the data to (as done in homeworks) i) ii) b) i. ii. 111. iv. normal pdf log-normal pdf Discuss, if and why, any one particular pdf is more suitable in your case. Determine in each of the cases in (a) its mean, mode, and median. For each pdf, determine the warranty period. What is your 80% confidence interval for the mean values? If she makes the warranty to be the MTTF, what would your percentage of profit/loss would be? If the aborted tests had been continued until failure, determine the probability of the units surviving 5 more months since the aborted time. Team: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 $m 100 125 150 175 200 200 175 150 125 100 100 125 150 175 200 200 175 150 125 100 100 125 $s 150 180 230 260 300 300 260 230 190 150 160 190 230 260 300 310 270 230 190 150 150 190 ToF (months) 23.3 2.9 18.8 10.2 4.2 15.4 19.1 19.9 13.2 20.8 19.8 10.3 12.6 22.5 15.3 4.9 0.1 3.9 17.2 18.5 6.9 21.8 1.4 23.3 7.8 3.7 6.3 11.5 16.2 4.5 16.4 19.7 17.0 0.1 9.6 5.4 10.5 23.4 7.8 14.3 2.9 5.6 12.7 18.6 red entries 17.4 10.2 5.5 0.7 11.1 4.1 6.6 15.8 15.7 18.0 2.4 15.9 4.5 8.4 20.1 1.5 4.0 21.2 19.8 22.5 17.8 9.0 indicate aborted 17.3 7.9 14.9 21.9 10.3 15.6 7.4 E 1.1 13.0 7.2 24.0 5.1 0.6 15.7 22.1 4.7 9.1 3.8 21.8 16.3 1.9 tests 5.1 7.7 23.4 21.6 17.3 16.1 12.7 0.2 23.4 18.6 15.0 6.7 19.8 22.6 18.2 12.6 16.9 13.5 3.6 14.2 8.0 196 11.1 9.5 17.3 1.6 6.6 10.1 15.2 15.1 21.1 4.9 14.0 13.0 3.9 8.1 7.3 15.5 24.9 18.7 6.0 19.8 21.4 15.5 6.9 11.8 7.8 13.3 19.3 5.7 19.0 23.0 11.9 13.6 8.4 23.5 17.6 9.7 23.2 20.7 7.4 5.9 16.8 24.1 8.4 18.0 21.6 16.8 22.8 19.7 9.3 9.9 638 6.8 14.8 14.1 19.2 1.8 15.6 20.1 11.2 24.1 22.5 15.6 21.9 15.2 10.8 14.1 14.0 21.1 13.0 24.9 6.2 9.9 13.9 1.8 13.0 12.3 5.5 14.6 1.0 21.2 14.4 19.3 8.8 20.6 23.8 22.4 15.4 24.4 23.8 4.4 1.0 3.1 5.3 9.9 17.8 13.7 16.8 15.4 19.9 9.7 18.8 9.0 0.3 9.3 18.8 0.2 12.5 22.0 22.7 15.9 4.4 9.7 8.2 9.5 21.9 7.4 20.2 12.0 16.1 21.4 23.5 24.2 5.6 10.1 20.0 19.9 23.3 24.3 20.5 18.2 20.5 9.9 18.0 4.8 18.5 10.8 8.8 8.5 1.5 4.3 7.2 5.1 8.6 2.6 17.0 20.3 18.4 21.3 1.3 6.8 20.4 23.8 14.8 19.0 13.1 7.1 23.5 8.3 17.9 3.5 17.3 5.0 18.0 11.7 7.7 21.2 17.3 2.1 23.0 13.1 11.0 15.6 4.3 7.7 15.6 0.4 22.2 9.9 17.3 1.1 3.3 11.8 17.2 3.0 8.7 22.3 10.4 4.0 9.0 19.8 5.6 18.8 15.2 8.3 9.3 10.3 22.7 8.8 2.1 13.2 19.7 19.1 19.5 22.2 12.7 13.5 6.3 4.0 24.3 2.9 9.5 9.9 17.6 10.6 16.3 23.0 16.3 12.3 19.7 11.8 19.2 12.7 14.1 6.8 5.7 11.8 19.1 24.2 17.5 8.6 2.6 6.7 7.7 3.5 4.5 3.9 11.6 3.5 19.8 9.6 16.8 13.6 8.3 2.0 12.9 22.1 5.1 0.1 12.5 24.8 20.1 0.1 9.9 11.4 21.8 11.1 1.8 14.4 16.9 6.7 11.2 19.0 9.0 10.8 16.4 6.7 19.5 5.6 19.2 20.1 1.5 23.4 24.1 5.9 7.7 14.0 25252 17.4 22.8 14.1 16.0 12.0 22.6 6.5 16.3 19.0 19.1 20.7 20.5 15.6 19.9 18.7 8.0 18.5 4.7 16.3 18.8 5.7 16.5 15.8 9.6 1.3 12.9 1.5 17.9 15.5 23.4 15.5 18.5 9.3 12.6