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

Sample Service Life $($hours$)$

$1495500505500$

$2525515505515$

$3470480460470$

What is the standard deviation of the sampling distribution of sample means for whenever service life is in control?

Group of answer choices

$5$ hours

$6\mathrm{.}67$ hours

$10$ hours

$11\mathrm{.}55$ hours

$20$ hours