Fusion Beverages LLC has been contracted to produce PowerBoost, which is a new energy drink that the artist SonicGroove has formulated. The recipe requires 100 milligrams of taurine in each 16-ounce bottle. To ensure compliance, Alex Terry, the quality control manager at Fusion Beverages, has selected eight bottles of PowerBoost from its last eleven batches and conducted taurine content tests. The data from these tests is as follows:

1. what is the upper control limit for the R-chart (i.e., UCL_R)?
2. what is the upper control limit for the x-bar chart (i.e., UCL_X)?

5. Is the process for making EnerD considered in control? Select ONE.

a. Yes, because all points on the R-chart are within the control limits

b. Yes, because all points on the R-chart AND X-bar chart are within the control limits

c. No, because points on the R-chart OR X-bar chart are not within the control limits

d. No, because points on the R-chart OR x-bar chart are too close to the center line
 

Batch Bottle 1 1 103.87 2 101.5 3 4 5 6 7 8 9 10 11 103.8 101.5 101.85 98.55 97.15 107.65 Bottle 2 Bottle 3 104.15 104.52 99.42 96.22 100.11 101.46 99.73 107.81 104.62 107.62 98.58 96.85 92.11 Mg taurine per bottle Bottle 4 Bottle 5 104.9 107.5 101.47 103.42 101.48 98.3 97.75 107.52 104.07 105.5 97.5 101.4 98.96 103.56 100.89 96.65 98.36 102.75 104.95 94.63 99.87 109.2 102.1 99.25 100.89 106.28 96.58 99.19 103.15 111.58 104.33 100.89 102.01 96.95 Bottle 6 107.15 96.15 99.75 Bottle 7 99.12 109.52 100.22 107 100.35 108.5 103.83 97.66 100.55 101.84 107.85 102.62 98.76 103.18 101.25 104.45 103.06 102.98 99.33 Bottle 8 110.5 94.3 102.2 96.93 105.11 110.07 105.48 101.67 105.36 104.71 98.87