Problem 1 (10 points). The operator of automated sorting machines in a post office must read the zip code on letters and divert the letters to the proper carrier routes. Over a month's time, 12 samples of 100 letters were chosen and the proportions of errors were recorded as: 04, 02, 03, 02, 03, 03, 02, 01, 04, 05, 03 and .04. a. Calculate p-bar (CL) and the standard deviation of the process. (4) b. Calculate the control limits for a p control chart. (3) c. A sample of 100 letters has just been taken, and 9 errors were found. Is the process still in control? (3) Problem 2 (10 points). A company periodically tests its product for tread wear under simulated conditions. Thirty random samples, each containing 5 items, were taken in a control chart application and it was found that the grand average is x= 5.240 cm and R = 0.35. a. What would be the upper and lower control limits for the x and R charts. (7) b. The following measurements are taken last week: 5.2. 4.5.5.5.3.4.5.3, and 5.5. Is the process still in control? (3) Problem 3 (20 points). A candy store has sold the following number of pounds of candy for the past three days. Assuming a = 0.1, complete the following table. You must provide details of calculations for each entry filled in the table to earn credit. Period D F et MAD: 10 Tracking Signal 200 180 192