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 when this service life is in control it 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$)],[1,495,500,505,500,],[2,525,515,505,515,],[3,470,480,460,470,]]$

What is the upper control limit $($UCL$)$ if the value of $A_2$ is $0\mathrm{.}73?$

$500\mathrm{.}73$

$10\mathrm{.}95$

$361\mathrm{.}35$

$507\mathrm{.}17$

$484\mathrm{.}05$