Consider a bottling plant. One product they sell is orange juice in 32 oz bottles. The amount of juice in a bottle is one of the quality metrics they measure. When the process was known to be under control, the company collected six samples with five measurements in each. Below is that data:

	Sample
Measurement	1	2	3	4	5	6
1	31.2	32.32	32.16	32.32	32.16	32.32
2	31.36	32.48	32.32	31.84	31.2	32.8
3	31.84	31.84	31.36	32.8	32	32.32
4	32.32	32.32	32.16	31.84	31.68	32.64
5	32.64	31.2	31.68	31.36	32.64	31.84

1. Please calculate the upper and lower control limits for the Xbar and R charts the company can use to monitor if the process is remaining in control.
2. A few weeks later, the quality manager collected the following three samples. Is the process still in control? Please answer using the control charts you developed for part (i).

	Measurement
Sample	1	2	3	4	5
1	31.04	31.36	31.36	32	31.68
2	33.12	31.68	31.68	31.84	32.48
3	30.88	32.32	32.8	32	31.2

Part b

Due to increasing demand, the bottling plant is considering outsourcing some jobs. A supplier they are vetting has a bottle-filling process capable of filling bottles with a mean of 32.5 ounces and standard deviation of 0.25 ounces. The bottling company has set their internal standards at a target value as 32 ounces and the upper and lower tolerance limits as 32.8 and 31.2 ounces per bottle, respectively.

1. Is the supplier's process capable of meeting the botting company's standards? Please provide the necessary calculations to back your response.
2. Is the process more likely to produce bottles with more or less than 32 ounces of juice? Please explain your answer
3. After some process improvement efforts, the supplier's bottling process is now operating with a mean of 32 ounces (standard deviation remained the same). Is the process in capable now? Please justify your answer.