Variability $in$ Transit Time

You have $to$ select a transportation carrier $to$ use for replenishing your inventory. Demand for the item $is$ distributed Normally with a mean $of500$ units and a standard deviation $of100$ units per week. The cost $of$ the item $to$ include delivery $is$ $$450.$ You want a $CSLof95\%.$

Option $1$: Delivery leadtime mean$=4$ weeks, StdDev $=1$ week

Option $2$: Delivery leadtime mean$=4$ weeks, StdDev $=0\mathrm{.}5$ week

Option $3$: Delivery leadtime mean$=3$ weeks, StdDev $=1$ week

$Q1$: Suppose you decide $to$ use Option $1?$ What $is$ the average safety stock $in$ items? Enter your answer rounded $UPto$ the nearest integer.

$Q2$: Suppose you decide $to$ use Option $2?$What $is$ the average safety stock? Enter your answer rounded $UPto$ the nearest integer.

$Q3$: Suppose you decide $to$ use Option $3?$ What $is$ the average safety stock? Enter your answer rounded $UPto$ the nearest integer.

$Q4$: You have noticed how much impact that reliable transportation $(lead)$ time has $on$ your safety stock levels. You want $to$ understand how much more reliable Option $3(3$ weeks average and $1$ week standard deviation$)$ would need $tobeto$ match the safety stock needed $in$ Option $2.$ What would Option $3\text{'}s$ new standard deviation $of$ transit time need $tobeto$ have the same safety stock level $asin$ Option $2?$ Enter your answer $as$ a decimal.