This is a group assignment. Only one submission per group can be submitted. The objective of the assignment is for the group to figure out the requirements of the assignment and not contact me as a shortcut. If there is someone in the group who does not carry their weight then the appropriate action is to email me with that information and I will follow up$.$ If you do not participate then you will not receive the allocated points. IT IS A GROUP project. No Individual or sub submissions accepted. If you wait until $48$ hours before the assignment is due...I will be nonresponsive. To receive full credit there should be a $"$X and $"$R$"$ graph. The points should be labeled. You must tell me if the sample is within acceptable limits $($compliance$).$ The lines on the graph must be discernible.

Assignment $1$

A drive$-$in restaurant is running a new promotion, the "Route $44,"$ named after an interstate that runs through their primary market area. The drink is promoted as $44$ ounces of pure carbonated pleasure but the regional manager, being somewhat of a quality expert, wants to make sure that the company's drink process can deliver $44$ ounces. He decides statistical quality control is the best way to monitor their process.

For ten consecutive days he purchases five Route $44$ drinks from franchise locations on his way to headquarters and turns them over to the testing lab for volume analysis. The data appear in the table, all amounts are in fluid ounces as measured by the testing lab.

$\backslash$table$[[$Sample$,$Drink $1,$Drink $2,$Drink $3,$Drink $4,$Drink $5],[1,43\mathrm{.}51,41\mathrm{.}47,42\mathrm{.}15,48\mathrm{.}15,47\mathrm{.}14],[2,47\mathrm{.}94,47\mathrm{.}90,49\mathrm{.}72,48\mathrm{.}68,41\mathrm{.}71],[3,42\mathrm{.}05,44\mathrm{.}65,47\mathrm{.}37,41\mathrm{.}43,48\mathrm{.}32],[4,41\mathrm{.}72,47\mathrm{.}94,46\mathrm{.}68,43\mathrm{.}13,40\mathrm{.}62],[5,46\mathrm{.}98,48\mathrm{.}39,41\mathrm{.}30,46\mathrm{.}52,43\mathrm{.}44],[6,40\mathrm{.}83,42\mathrm{.}44,48\mathrm{.}94,46\mathrm{.}74,41\mathrm{.}83],[7,48\mathrm{.}76,41\mathrm{.}65,46\mathrm{.}41,44\mathrm{.}73,48\mathrm{.}41],[8,49\mathrm{.}53,46\mathrm{.}18,49\mathrm{.}65,40\mathrm{.}11,47\mathrm{.}08],[9,43\mathrm{.}42,41\mathrm{.}16,46\mathrm{.}53,48\mathrm{.}23,47\mathrm{.}63],[10,46\mathrm{.}56,41\mathrm{.}10,41\mathrm{.}04,40\mathrm{.}56,43\mathrm{.}06]]$

Since the regional manager is somewhat of a quality expert, he needs your help in formulating a control chart that will monitor the process performance to target. Develop the appropriate limits and create a chart. Is the process in control?