An automatic filling process is used to dispense hand sanitizer into small purse size bottles. The target weight is 75 ml. The company has initiated control charting to stabilize and improve the automatic filling process. For each of twenty-five samples consisting of four bottles, the contents were measured and the mean weight and range were determined. The average of the means across all samples was found to be 72.5 ml. and the average range was 2.75 ml. The control limits for the x-bar chart are
A) 68.48 and 76.52 ml.
B) 71.16 and 73.84 ml.
C) 70.50 and 74.50 ml.
D) 72 and 73 ml.
E) 66.84 and 78.16 ml.

Question

Quizplus · Accepted Answer

Based on the given information, the control limits for the x-bar chart can be calculated as follows:

Upper control limit (UCL) = X̄ + A2R = 72.5 + (0.577)(2.75) = 74.5 ml
Lower control limit (LCL) = X̄ - A2R = 72.5 - (0.577)(2.75) = 70.5 ml

Therefore, the appropriate choice is C.

An Automatic Filling Process Is Used to Dispense Hand Sanitizer