31. Beaver Brothers, Inc., is condu

31. Beaver Brothers, Inc., is conducting a study to assess the capability of its 150-gram bar soap production line. A critical quality measure is the weight of the soap bars after stamping. The lower and upper specification limits are 162 and 170 grams, respectively. As a part of an initial capability study, 25 samples of size 5 were collected by the quality assurance group and the observations in Table 3.7 were recorded. After analyzing the data by using statistical control charts, the quality assurance group calculated the process capability ratio, Cp, and the process capability index, Cpk. It then decided to improve the stamping process, especially the feeder mechanism. After making all the changes that were deemed necessary, 18 additional samples were collected. The summary data for these samples are x = 163 gramsR = 2.326 gramss = 1 gramAll sample observations were within the control chart limits. With the new data, the quality assurance group recalculated the process capability measures. It was pleased with the improved Cp but felt that the process should be centered at 166 grams to ensure that everything was in order. Its decision concluded the study.a. Draw the control charts for the data obtained in the initial study and verify that the process was in statistical control.b. What were the values obtained by the group for Cp and Cpk for the initial capability study? Comment on your findings and explain why further improvements were necessary.c. What are the Cp and Cpk after the improvements? Comment on your findings, indicating why the group decided to change the centering of the process.d. What are the Cp and Cpk if the process were centered at 166? Comment on your findings。