Sally$$s Silk Screening produces specialty T$-$shirts that are primarily sold at special events. She is trying to decide how many to produce for an upcoming event. During the event, Sally can sell T$-$shirts for $$53$ apiece. However, when the event ends, any unsold T$-$shirts are sold for $$17$ apiece. It costs Sally $$34$ to make a specialty T$-$shirt. Sally$$s estimate of demand is the following:

DEMAND PROBABILITY

$3500\mathrm{.}05$

$4250\mathrm{.}07$

$5250\mathrm{.}32$

$5500\mathrm{.}40$

$5850\mathrm{.}11$

$6500\mathrm{.}05$

a$.$ What is the service rate $($or optimal fractile$)?($Round your answer to $2$ decimal places.$)$

b$.$ How many T$-$shirts should she produce for the upcoming event?