Samples of five dowel pins were evaluated for pin length. The average and standard deviations were calculated for each sample. After 25 consecutive samples were evaluated, a grand average, an average standard deviation, and an average range were computed to be 25.671mm, 0.130mm, and 0.78mm, respectively. (a) Determine the appropriate preliminary three sigma control limits for monitoring the mean of this production process. Show calculations. (b) Determine the appropriate preliminary three sigma control limits for monitoring the variability of this production process. (c) Assume the dowel pin lengths to be in control with regard to both central tendency and variability. The next sample results in the following pin lengths: 25.78, 25.77, 25.72, 25.77, 25.81. Do the length statistics fall within the control limits? (d) Continued from (c) above but assume that you work for an European company. Would the same conclusions regarding the pin lengths be drawn? Why do you think so?