Factors for calculating three-sigma limits for the x-chart and R-chart Factor for LCL for R-Chart (D3) Size of Sample Factor for UCL and LCL for X-chart (A2) 2 1.880 3 1.023 4 0.729 5 0.577 6 0.483 7 0.419 8 0.373 9 0.337 10 0.308 0 0 0 0 0 0.076 0.136 0.184 0.223 Factor for UCL for R-Chart (D4) 3.267 2.575 2.282 2.115 2.004 1.924 1.864 1.816 1.777 A critical dimension of the service quality of a call center is the wait time of a caller to get to a sales representative. Periodically, random samples of three customer calls are measured for time. The results of the last four samples are in the following table: Time (sec) 2 3 Sample 1 2 1 497 504 510 491 495 503 506 494 490 502 502 500 3 4 Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. a. Assuming that management is willing to use three-sigma control limits, and using only the historical information contained in the four samples, show that the call center access time is in statistical control. Since all the sample ranges are between UCLR = seconds and LCLR = seconds and all of the sample means are between UCL = seconds and LCL:=seconds, the call center access time is in statistical control. (Enter your responses rounded to two decimal places.) b. Suppose that the standard deviation of the process distribution is 8.01. If the specifications for the access time are 500 17 seconds, is the process capable? Why or why not? Assume three-sigma quality. O A. Yes, because Cpk is greater than the critical value of 1.0. O B. No, because Cpk is greater than the critical value of 1.0. This is because the process variability did not meet the three-sigma target. OC. No, because Cpk is greater than the critical value of 1.0. This is because there are too many times outside of the allowable tolerances. OD. No, because Cpk is less than the critical value of 1.0. This is because the process is not centered correctly. O E. No, because Cpk is less than the critical value of 1.0. This is because there are too many times outside of the allowable tolerances