QUESTION $1$

A$.$ Battery manutacturer has recently received compleints from retailors that its $9-$volt batteries are not lasting as long as other name brands. Jabu Xuk, the Quality execuslvo believes that there is no problem because his batteries have had an average te of $50$ hours, which is about $10\%$ longer thet competilor's modes. To raise the lifetime above this level would require a new lovel of lechinology not available to this batlery manufacturer. Nevertheless, he is concerned enough to set up hourly assembly line checks. Previously, after ensuring that the process was running property, the company collected samples data of $9-$volta batterias. Those samples are shown in tha table following table

$\backslash$table$[[$HOUR$,$SAMPLES$],[1,2,3,4,5],[1,51,50,49,50,50],[2,45,47,70,46,36],[3,50,35,48,39,47],[4,35,70,50,30,51],[5,49,38,64,36,47],[6,59,62,40,54,64],[7,36,39,49,48,56],[8,50,67,53,43,40],[9,44,52,46,47,44],[10,70,45,50,47,41],[11,57,54,62,45,36],[12,56,54,47,42,62],[13,40,70,58,45,44],[14,52,58.,40,52,46],[15,57.,42,52,58,59],[16,62,49,42.,33,55],[17,40,39,49.,59,48],[18,64,50,42,5.,50],[19,58,53,52,48,50],[20,$BO$,50,41,41,50],[21,52,47,48,59,40],[27,55,40,58,49,45],[23,47,48,50,50,48],[24,50,60,49,51,51],[25,51.,50,59,51,62],[26,48,52,39,57,61],[27,46,53,48,46,66],[28,63,49,50,45,53],[29,57,70,45,52,61],[30,45,34,46,54,52]]$

$1,1$ Which control charts must be used to analyze the above data? Justify you answer

$(4)$

$12$ Calculate the means and the appropriate controllimits.

$(20)$

$1\mathrm{.}3$ Draa the approprlate control charts NB: Cloarly labol your charts.

$(14)$

$1$ A Has the manufacturing process been in cortrel? Why?

$(6)$