Shampoox Company produces organic shampoo. The product is produced and then filled into plastic shampoo bottles. The production manager is concerned whether the filling process for shampoo bottles is in statistical control. The process should be centered on 8 ounces per bottle. Six samples of size 5 were taken and each bottle was weighted. The weights are:

Ounces of Shampoo per bottle
2 3 4 8.34 8.24 7.23 7.87 8.12 8.21 7.78 7.76 7.56 8.21 8.23 7.76 7.78 7.89 8.02 7.98 5 8.12 7.99 8.1 8 8.02
Sample 7.87 8.03 7.78 1 7.78 7.89 8.22 8.02 7.77

Guideline: Follow procedures for constructing control charts and use A2, D3, and D4 tables.

a) Find the sample average and range for each of the six samples. 3

b) Construct the control limits of the X-bar chart. Is there any out of control sample?

c) Construct the control limits of the R-chart. Is there any out of control sample? If there is, what would you do? Explain with one sentence.