1. A service process is monitored using x-bar and R charts. Ten samples of n=9 observations have been gathered with the following results: Sample 1 2 3 Mean 4.21 3.74 3.68 Range 1.03 1.17 0.96 4 3.81 1.68 5 6 7 8 9 10 4.18 3.84 4.07 3.73 3.42 3.56 0.96 1.42 1.11 0.92 1.13 1.15 a. Using the data in the table, compute the center line, the upper control limit, and the lower control limit for the x-bar and R charts. b. Is the process in control? c. If the next sample results in the following values, will the process be in control? 3.75 2.79 4.28 3.77 4.31 3.43 2.21 4.15 2. A finishing process packages assemblies into boxes. You have noticed variability in the boxes and want to improve the process to fix the problem because some products fit too tightly and others too loosely. Following are the width measurements for the boxes. 1 2 3 4 5 6 7 8 78.752 79.387 79.523 78.622 78.452 78.894 77.250 77.830 79.490 79.864 77.767 79.980 77.559 78.523 78.356 78.369 79.851 77.399 77.946 78.094 79.100 77.209 77.106 79.952 77.896 78.171 77.554 77.175 78.019 78.788 79.974 77.328 78.945 77.522 78.906 79.673 78.214 78.336 77.401 77.562 78.291 77.881 79.634 79.792 79.318 78.730 79.756 79.070 77.254 79.553 79.979 79.921 77.235 77.665 78.741 78.094 a. Using the data in the table, compute the center line, the upper control limit, and the lower control limit for the x-bar and R charts. b. Is the process in control? 3. The following data was gathered to establish control charts for a process. 1 2 3 4 5 6 7 8 9 10 234 228 220 235 229 233 233 215 235 223 218 216 224 229 226 224 232 228 235 233 229 215 227 234 232 218 228 217 216 216 223 224 218 229 217 219 221 223 233 234 224 219 219 228 228 218 221 225 228 234 223 230 217 234 224 222 229 232 219 221 228 217 225 231 220 225 217 230 227 235 231 226 222 235 233 228 231 217 226 220 a. Using the data in the table, compute the center line, the upper control limit, and the lower control limit for the x-bar and R charts. b. Is the process in control