(Solved): Auto pistons at Wenming Chung's plant in Shanghai are produced in a forging process, and the diame ...

Auto pistons at Wenming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) What is the value of \( \bar{x} \) ? \( \overline{\bar{x}}=\quad \mathrm{mm} \) (round your response to two decimal places). b) What is the value of \( \bar{R} \) ? \( \overline{\mathrm{R}}=\mathrm{mm} \) (round your response to two decimal places). c) What are the \( U \mathrm{CL}_{\bar{\chi}} \) and \( \mathrm{LCL}_{\bar{\chi}} \) using 3-sigma? Upper Control Limit \( \left(\mathrm{UCL}_{\bar{\chi}}\right)=\mathrm{mm} \) (round your response to two decimal places). Lower Control Limit \( \left(\mathrm{LCL}_{\overline{\mathrm{x}}}\right)=\mathrm{mm} \) (round your response to two decimal places). d) What are the \( \mathrm{UCL}_{R} \) and \( \mathrm{LCL}_{R} \) using 3-sigma? Upper Control Limit \( \left(\mathrm{UCL}_{R}\right)=\mathrm{mm} \) (round your response to two decimal places). Lower Control Limit \( \left(\mathrm{LCL}_{R}\right)=\mathrm{mm} \) (round your response to two decimal places).