In order to evaluate a packaging machine's performance, 30 samples of 50 units each were randomly selected from the process, a total of 347 defective packages were observed. A fraction nonconforming control chart was created to monitor the performance of such machine and it was reached that the packaging process was out of control. The control limits have been revised by eliminating the 19th, 24th, and 29th samples and corresponding defective packages counts (22, 20 and 24, respectively) that caused the process to be out of control. Afterwards, some improvements were made in order to reduce the variability of packaging machine's performance and 24 samples of 50 units each were selected from the process and a total of 133 defective packages was observed. Can you validate that the improvements made are satisfactory? {use a=0.05) [20p] In order to evaluate a packaging machine's performance, 30 samples of 50 units each were randomly selected from the process, a total of 347 defective packages were observed. A fraction nonconforming control chart was created to monitor the performance of such machine and it was reached that the packaging process was out of control. The control limits have been revised by eliminating the 19th, 24th, and 29th samples and corresponding defective packages counts (22, 20 and 24, respectively) that caused the process to be out of control. Afterwards, some improvements were made in order to reduce the variability of packaging machine's performance and 24 samples of 50 units each were selected from the process and a total of 133 defective packages was observed. Can you validate that the improvements made are satisfactory? {use a=0.05) [20p]