$2.$ Weekly Demand for HP printers at Alghanim Electronics store is normally distributed, with a mean of $250$ and standard deviation of $150.$ The store manager continuously monitors inventory and currently orders $1,000$ printers each time the inventory drops to $600$ printers. HP currently takes two weeks to fill an order. a$)$ How much safety inventory does the store carry? What cycle service level $($CSL$)$ does Alghanim Electronics achieve as a result of this policy? b$)$ Assume that the supply lead time from HP is normally distributed, with a mean of $2$ weeks and a standard deviation of $\backslash (1\mathrm{.}5\backslash )$ weeks. How much safety inventory should Alghanim Electronics carry if it wants to provide a CSL of $95\backslash \%?$ How does the required safety inventory change as the standard deviation of lead time is reduced from $\backslash (1\mathrm{.}5\backslash )$ weeks to zero in intervals of $\backslash (0\mathrm{.}5\backslash )$ weeks?