A quality inspector took five samples, each with four observations, of the length of a part (in centimetres). She computed the mean of each sample (see table below). a. Use the following data to obtain three sigma (i.e., z = 3) control limits for sample mean. Is the process in control? b. If a new sample (sample 6) has values 12.10, 12.19, 12.12, and 12.14, using the sample mean control chart in part a, has the process mean changed (i.e., is there an assignable variation)? It is known from previous experience that the standard deviation of the process is 0.02 cm. Sample Observation 1 1 2 3 4 5 12.11 12.15 12.09 12.12 12.09 2 12.10 12.12 12.09 12.10 12.14 3 12.11 12.10 12.11 12.08 12.13 4 12.08 12.11 12.15 12.10 12.12 X 12.10 12.12 12.11 12.10 12.12