Auto pistons at JE Piston's plant in Melbourne are produced in a foreign process, and the diameter is a critical factor that must be controlled. From a sample size of 1000 pistons produced each day, the mean and the range of this diameter has been at follows

Q17.	Day	Mean mm	Range mm
	1	156	4.2
	2	153	4.6
	3	152	4.1
	4	155	5
	5	157	4.5

a. what is the value of X =?

b. what is the value of R =?

c. what is the UCLx and LCLx using 3 standard deviation? 

d. what is the UCLR and the LCLR using 3 standard deviation? 

e. Is it true the diametere mean should be 154m, and you want this as your center (nominal) line, what are the new UCLx and LCLx?