Soft Derma Care Company (SDCC) manufactures and distributes various skin ointments. One of their products is the "90 grams protective healing ointment for cracked or extra dry skins." Answer the following 3 questions regarding the production process of this product. Note that each part is independent of each other. (a) In an effort to statistically control the production process of this product, ten jars of ointments are randomly picked from the filling plant every hour. The measurements (in grams) are recorded sequentially for the samples over the 12 hours of operation. The overall average of the 12 sample means is 89.9465 grams. The overall average of the 12 sample ranges is 0.3872 grams. Three sigma control limits are applied in the statistical process control of this item. Determine the upper and lower control limits of the X-bar chart and R-chart. (b) SDCC wants to ensure that the production process produces products (Dry skin care ointments) within acceptable tolerance limits where each jar has 900.3215 grams of ointment. To test this, the operator takes several sample measurements and determines the process' mean to be 89.9765 grams with a standard deviation of 0.1181 grams. Calculate and interpret the process capability index. What percent of the current production is expected to be within the given tolerance limits? (c) SDCC is trying to improve its production process. They set a policy for quality control that any jar filled less than 89.9960 grams will be considered underfilled (defective). A random sample of 520 jars picked daily over the past six days. The daily number of underfilled (defectives) jars are as follows: With this kind of data, which type of process control chart is the most appropriate? Specify the process control limits for which one would expect that only 2% of the production will fall outside these control limits