Use Table $14\mathrm{.}1.$ You are the owner of Hotspices.com, an online retailer of hip, exotic, and hard$-$to$-$find spices. Consider your inventory of saffron, a spice $($generally$)$ worth more by weight than gold. You order saffron from an overseas supplier with a shipping lead time of four weeks and you order weekly. Average weekly demand is normally distributed with a mean of $40$ ounces and a standard deviation of $30$ ounces.

a$.$ Suppose it uses an order$-$up$-$to level of $301$ ounces. What is its expected on$-$hand inventory?

Note: Use Table $14\mathrm{.}1.$ Round your calculated $\backslash (\backslash$mathbf$\{$z$\}\backslash )$ value to the nearest $0\mathrm{.}1$ increment. Round your answer to the nearest integer.

Expected on$-$hand inventory

b$.$ Suppose it uses an order$-$up$-$to level of $250$ ounces. What is its expected on$-$order inventory?

Note: Round your answer to the nearest integer.

Expected on$-$order inventory

c$.$ Suppose it uses an order$-$up$-$to level of $368$ ounces. What is its in$-$stock probability?

Note: Use Table $14\mathrm{.}1.$ Round your calculated $\backslash ($ z $\backslash )$ value to the nearest $0\mathrm{.}1$ increment. Round your answer to $4$ decimal places.

In$-$stock probability

d$.$ Suppose it wants a $0\mathrm{.}96$ in$-$stock probability. What should its order$-$up$-$to level be$?$

Note: Use Table $14\mathrm{.}1.$ Choose the $\backslash ($ z $\backslash )$ value with a cumulative probability AT LEAST as high as the required in$-$stock probability $($e$.$g$.,$ if in$-$stock probability is $0\mathrm{.}92,$ use $\backslash ($ z$=1\mathrm{.}5\backslash )$ instead of $\backslash ($ z$=1\mathrm{.}4\backslash )).$ Round your answer to the nearest integer.

Order$-$up$-$to level