The gross claim cost for an insurance company in $2006$ on an automobile policy is the sum of three independent components:

a$.$ Repair costs, with a mean of $2,500$ and a standard deviation of $500$

b$.$ Legal costs, with a mean of $4,000$ and a standard deviation of $2,000$

c$.$ Fixed expenses of $250$

The inflation from $2006$ and $2007$ was $5\%$ for repair costs, $10\%$ for legal costs, and $8\%$ for fixed expenses. Calculate the standard deviation of the gross claim cost in $2007.$

a

$2,159$

b

$2,262$

c

$2,971$

d

$3,263$