A design engineer wants to construct a sample mean chart for controlling the service life of one of the types of light bulbs 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 bulbs, with these results:

Sample SERVICE LIFE $($hours$).$

If he uses upper and lower control limits of $505$ and $470$ hours, on what sample$($s$)($if any$)$ does service life appear to be

out of control?

Sample $1$

Sample $2$

Sample $3$

Samples $1$ & $3$

The correct answer is not provided.