A company that produces and distributes electronic equipment in the Northeast, currently partitions the region into two markets. Each market is served by a single warehouse $($i$.$e$.,$ each customer is assigned to a single market and receives deliveries from the warehouse in that region$).$

The following information is the historical weekly demand at each region$/$market for a typical product: $$Product X$($assume $50$ weeks per year$).$ Note that the ordering cost is $$300$ per order, lead time is always $4$ weeks, carrying cost is $$30$ per unit per year, the desired service level is $95\%,$ and they are utilizing a continuous review inventory system. The company has decided to serve both markets$/$regions by utilizing a single centralized warehouse.

Table $1-$ Weekly Demand Data

Week

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

Market $1$

$75$

$62$

$70$

$65$

$58$

$74$

$53$

$77$

$70$

$76$

Market $2$

$78$

$93$

$71$

$98$

$65$

$79$

$66$

$95$

$90$

$80$

The average demand at the centralized warehouse is $154\mathrm{.}5$ units per week.

Calculate the standard deviation of the demand at the centralized warehouse