A quality control inspector at the Beautiful Shampoo Company has taken three sam

Question

A quality control inspector at the Beautiful Shampoo Company has taken three samples with four observations each of the volume of shampoo bottles filled. The data collected by the inspector and the computed means are shown here:

If the standard deviation of the shampoo bottle-filling operation is 0.2 ounces, use the information in the table to develop control limits of 3 standard deviations for the operation: (a)CL, (b) UCL, (c) LCL. (Round answers to 2 decimal places, e.g. 15.25.)

Samples of Shampoo Bottle Volume in Ounces Observation 1 2 3 1 19.7 19.7 19.7 2 20.6 20.2 18.7 3 18.9 18.9 21.6 4 20.8 20.7 20.0 Mean 20.0 19.875 20.0

Explanation / Answer

UCL=X1+z LCL=X1-z

=0.2/2

X1=Average of sample means

X1=(20+19.875+20)/3= 19.95

So UCL = 19.95+ 3( 0.2/2)=19.95+0.3= 20.25

LCL= 19.95-0.3= 19.65

CL= 19.95

UCL=X1+z LCL=X1-z

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