Question $2(15\%)$:The operations manager of Green Apple Juice Co$.$ is concerned about the quality of the companys $8-$ozbottle filling line and will track it$.$ The bottles need to be filled according to the specified tolerances for thisproduct because the nutritional details on the label indicate that the serving size is $8$ ounces. The product'sdesign standard specifies a fill level of $8\mathrm{.}00$ ounces, with a tolerance of $\backslash$pm $0\mathrm{.}067$ ounces. The managergathered nine observations and obtained the next samples data during the production process:Sample Fluid oz per bottleAverage Range$18\mathrm{.}030\mathrm{.}0927\mathrm{.}990\mathrm{.}1337\mathrm{.}980\mathrm{.}0948\mathrm{.}030\mathrm{.}1058\mathrm{.}030\mathrm{.}1368\mathrm{.}010\mathrm{.}0978\mathrm{.}020\mathrm{.}0688\mathrm{.}000\mathrm{.}0697\mathrm{.}990\mathrm{.}05107\mathrm{.}990\mathrm{.}11$a$.$ Calculate all the $-$ chart and R$-$chart limits for this process. Is the process in control? Explain.b$.$ The results for new three samples of $8-$oz bottle juice filling are:Page $11$ of $12$Sample Observation$12345678917\mathrm{.}987\mathrm{.}937\mathrm{.}938\mathrm{.}027\mathrm{.}957\mathrm{.}967\mathrm{.}957\mathrm{.}988\mathrm{.}0027\mathrm{.}977\mathrm{.}968\mathrm{.}048\mathrm{.}028\mathrm{.}017\mathrm{.}978\mathrm{.}058\mathrm{.}047\mathrm{.}9937\mathrm{.}957\mathrm{.}967\mathrm{.}907\mathrm{.}958\mathrm{.}008\mathrm{.}027\mathrm{.}967\mathrm{.}978\mathrm{.}01$Is the process in control? Explain.c$.$ Calculate the process capability ratio and the process capability index. Is the process capable of meetingthe design standard? Explain.d$.$ What percentage of $8-$oz bottle filling will lie within the control limits obtained in part a$,$ given the meanproducts design standard $($process distribution$)?$