Given this information:

i$.$ Expected demand during lead time $=500$ units.

ii$.$ Standard deviation of lead time demand $=50$ units.

Determine each of the following, assuming that lead time demand is distributed normally:

a$.$ The safety stock needed to attain a $1$ percent risk of stockout during lead time.

b$.$ The reorder point $($ROP$)$ that will provide a risk of stockout of $1$ percent during lead time.

c$.$ Would a stockout risk of $2$ percent require more or less safety stock than a $1$ percent risk? Show the numbers.

d$.$ Would the ROP be larger, smaller, or unaffected if the acceptable risk was $2$ percent instead of $1\%?$ Show the values.

Explain. NOTE: When standard deviation of the lead time demand is given, SS $=$ Z $*$ that value.