2. Suppose that South Tree Electronics is testing its circuit boards to see if they are defective or not and to determine if its circuit board production process is in control or not. Every hour, South Tree samples 25 circuit boards coming off of its production line and obtains the following results. Number Sample Sample Size Defective 25 6 25 3 25 10 25 12 25 {DmCmI-P-WMH ,,_. CD 25 10 a. Calculate the upper and lower control limits for the pchart associated with the above data. Use a zvalue of 3 in determining your control limits. b. Determine whether or not the circuit board production process is in control. If it is not in control, state what looks wrong on the p-chart. 3. Suppose that we are making paper and that the mean width of a sheet of paper is 2.6 mm with a variance of .06 mm2. We would like to set the upper and lower specication limits so that 96.06% of all sheets of paper fall within the upper and lower specication limits. Moreover, we would like the mean paper width to be centered halfway between the upper and lower specication limits. a. What should we set the upper and lower specication limits to be? (Assume that the width of a sheet of paper is normally distributed. You may need to use a z-table for this question.) b. Calculate the 0;, and the Cpk of the process