$1$

A design engineer wants to construct a sample mean chart for controlling the service life of of the types of light bulbs his company produces. The engineer knows from numerous previous samples that this service life is normally distributed with a mean of $500$ hours and a standard deviation of $20$ hours. On three recent production batches, the engineer tested service life on random samples of four bulbs, with these results:

$10$ points

$00$:$57$:$11$

$\backslash$table$[[$Sample$,$Service Life $($hours$)],[1,495,500,505,500],[2,525,515,505,515],[3,470,480,460,470]]$

eBook

If upper and lower control limits of $520$ and $480$ hours are used, on what sample$($s$)($if any$)$ does service life appear to be out of Control $?$