GameStop has maintained $75\%$ service level for inventory of PlayStation $5.$ Expected demand during lead time is $166$ PlayStations, and the standard deviation of demand during lead time is $58$ PlayStations. The annual cost of carrying one PlayStation $5$ in inventory is $$12.$ The store$$s operations analyst recently told GameStop's management that they could expect a $$550$ improvement in annual income if the service level were increased to $97\mathrm{.}5\%.$ However, when estimating the increase in income, the operations analyst did not consider the impact of additional safety stock carrying costs resulting from the change in the service level. Is it worthwhile for GameStop to increase the service level from $75\%$ to $97\mathrm{.}5\%?$