Daily demand for PCs at HP is normally distributed, with a mean of $1,000$ and a standard deviation of $200.$ A key component in PC assembly is the hard drive. The hard drive supplier takes an average of L $=3$ days to replenish inventory at HP$.$ HP is targeting a CSL of $90$ percent for its hard drive inventory. Evaluate the safety inventory of hard drives that HP must carry if the standard deviation of the lead time is four days. HP is working with the supplier to reduce the standard deviation to two. Evaluate the reduction in safety inventory that HP can expect as a result of this initiative.$[$ F$-1(90)=1\mathrm{.}28]$