Case $5(33$ p$.)($Round all your answers to four digits after the decimal point$)$ Q$1.(17$ p$.)$ ABC Ltd$.$ has recently been receiving complaints from retailers that their batteries are not lasting as long as other name brands. A quality manager decided, therefore, to take $28$ samples $($in randomly selected time intervals$)$ of the batteries $($each sample consisting of five batteries$)$ to establish the standards for relevant control chart limits$.$ The results are shown in the table below $($the numbers represent how many hours a battery lasted$)$: Sample no$.$ Battery $1$ Battery $2$ Battery $3$ Battery $4$ Battery $5149505148382364839474335062466452444454238475383636573965564515353764625548538475462424993655483538105139643743114540383740124342454848136454555650144546665538153854366455164539416344174845584539185564486543195139566551204763485352214355544739223852473946234348395647245537625553255145454839264251644950274153393745284750423646$ Determine the upper and lower control limits for all relevant charts. Show all your calculations. Q$2.(16$ p$.)$ One of the Airline XYZ Ltd$.$s top competitive priorities is on$-$time arrivals. Quality VP decided to personally monitor the company$$s performance in this area. Each week for the past $32$ weeks, she checked a random sample $($the samples varied in size across the weeks$)$ of flight arrivals for on$-$time performance. The table below contains the

Determine the upper and lower control limits for a relevant control chart. Show all your calculations.

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