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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.

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:
Day
Mean x
(mm)
Range R
(mm)
1
156.9
4.0
2
151.2
4.6
3
153.6
4.1
4
157.5
5.2
5
156.6
4.5
Part 2
a) What is the value of x?
x=155.16155.16 mm (round your response to two decimal places).
Part 3
b) What is the value of R?
R=4.484.48 mm (round your response to two decimal places).
Part 4
c) What are the UCLx and LCLx using 3-sigma?
Upper Control Limit (UCLx)=156.54156.54 mm (round your response to two decimal places).
Part 5
Lower Control Limit (LCLx)=153.78153.78 mm (round your response to two decimal places).
Part 6
d) What are the UCLR and LCLR using 3-sigma?
Upper Control Limit (UCLR)= enter your response here mm (round your response to two decimal places).

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