Weekly demand for HP printers at a Sam$$s Club store is normally distributed,

with a mean of $250$ and a standard deviation of $150.$ The store manager continuously

monitors inventory and currently orders $1,000$ printers each time the inventory drops to

$600$ printers. Assume that the supply lead time from HP is normally distributed, with a

mean of $2$ weeks and a standard deviation of $1\mathrm{.}5$ weeks. How much safety inventory should

Sam$$s Club carry if it wants to provide a CSL of $95$ percent? How does the required safety

inventory change as the standard deviation of lead time is reduced from $1\mathrm{.}5$ weeks to zero

in intervals of $0\mathrm{.}5$ weeks?