A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He 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, he tested service life on random samples of four headlamps, with these results:

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

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

Multiple Choice

both samples $2$ and $3$

sample $2$

sample $1$