PROBLEM 1 (30 points) State Coverage Insurance Company inspect their claim forms periodically for errors. Their goal is to have zero errors on any of their claim forms. If one or more errors are found within a form, it is considered noncomforming. The company would like to use statistical process control to determine if there is a lot of variation present in the process used to complete the forms. Over the course of the last 25 working day. 125 forms were inspected each day and the number of forms with errors (i.e., nonconforming forms) were recorded The table below provides the number of nonconforming forms found each day. Use the data to answer the following questions. Carry calculations out to at least 3 decimal places. Show your work. a. What is type of control chart(s) should be constructed based on the data provided in the table below on the left (i.e., C, P, X-bar, and/or R)? b. What is the central limit for this data? c. What are the 3-sigma upper and lower control limits? d. Construct the control chart showing not only the control limits but also the zone lines for the pattern test. Label the zones on the chart itself and identify the top and bottom border of each zone by completing the table below on the right. Note: The control chart may be created in Excel but a copy of it should be embedded as a picture in your test document. Make sure it is large enough to read all elements. e. State whether or not the process appears to be in control? Were any pattern test violations found? If so, identify them (name the pattern and which points fit the pattern). DATA COLLECTED ZONE INFORMATION TABLE # Nonconforming Zone Top boarder Bottom boarder A top B top C top C bottom B bottom A bottom