In awarding the construction contracts for the new Freedom Tower in New York City, the city contracted with your company to provide a specialized welding service for the steel girders for this project. Since the project must proceed according to a tight schedule, and thousands of welds must be made, welding times are critical. Data have been collected on 50 welding times that were observed during crew training sessions and are reflected in the table below. To receive certification, the requirement for all welders is to be able to produce high-quality welds in no more than 10 minutes.

a. Construct a histogram of the raw data. Comment on its normality and whether the process appears to be meeting the maximum welding time requirement.
b. Construct X and MR charts and comment on the state of statistical control.
c. Next, use a Box-Cox transformation with to generate a transformed pair of control charts and comment on control.
d. Using the raw data, estimate the mean and standard deviation of the process, and the percentage of welds that are likely to exceed 10 minutes. How confident are you in these estimates given your conclusions from part c?
e. Using the raw data, estimate the mean and standard deviation of the process, and the percentage of welds that are likely to exceed 10 minutes. How confident are you in these estimates given your conclusions from part c?

Welding Time (in mins) ObservationTime observation Time 10.2097 19.3935 6.6392 6.2914 16.0297 1.4671 1.3363 8.4815 7.1757 6.3445 16.4467 4.243 2.0252 5.3992 9.8326 7.4587 3.9621 3.3363 23.2068 26 27 28 29 30 31 32 4.555 10.950 8.639 15.234 6.383 6.356 6.880 4.020 1.414 7.906 5.438 6.002 20.764 13.196 1.373 10.641 .553 7.196 1.925 3.958 5.290 21.812 9.512 1.872 4 5 6 34 35 36 37 38 39 40 41 42 43 9 10 12 13 14 15 16 17 18 19 20 21 7.8671 45 46 47 48 49 50 1.3904 10.6189 6.2741 23 24 25 5.172 1454