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 of $500$ units and a standard deviation of $100$ units per week. The cost of the item to include delivery is $$450.$ You want a CSL of $95\%.$

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

Q$1$: Suppose you decide to use Option $1?$

What is the average safety stock in items? Enter your answer rounded UP to the nearest integer. $[$result: $886]$

Q$2$: Suppose you decide to use Option $2?$

What is the average safety stock? Enter your answer rounded UP to the nearest integer. $[$result: $527]$

Q$3$: Suppose you decide to use Option $3?$

What is the average safety stock? Enter your answer rounded UP to the nearest integer. $[$result $871]$

Q$4$: 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 to be to match the safety stock needed in Option $2.$

What would Option $3\text{'}$s new standard deviation of transit time need to be to have the same safety stock level as in Option $2?$ Enter your answer as a decimal.