Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma)

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for this problem.Auto pistons at Wemming 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

1010

pistons produced each day, the mean and the range of this diameter have been as follows:

Day	Mean Bold x overbarx (mm)	Range R (mm)
1	158.9158.9	4.24.2
2	151.2151.2	4.64.6
3	155.6155.6	3.93.9
4	155.5155.5	5.25.2
5	158.6158.6	4.74.7

a) What is the value of

x double overbarx?

x double overbarxequals=____mm (round your response to two decimal places).b) What is the value of

Upper R overbarR?

Upper R overbarRequals=_____mm (round your response to two decimal places).c) What are the

UCL Subscript x overbarUCLx and LCL Subscript x overbarLCLx using 3-sigma?

Upper Control Limit (UCL Subscript x overbarUCLx) =_______mm (round your response to two decimal places).Lower Control Limit

(LCL Subscript x overbarLCLx)=_______mm (round your response to two decimal places).d) What are the

UCL Subscript Upper RUCLR and LCL Subscript Upper RLCLR using 3-sigma?

Upper Control Limit(UCL Subscript Upper RUCLR) = ____mm (round your response to two decimal places).Lower Control Limit

(LCL Subscript Upper RLCLR)=_____mm (round your response to two decimal places).