TABLE $7-2$ Standard Deviations and Probabilities

$\backslash$table$[[\backslash$table$[[Z=$ Number of$],[$Deviations$],[$Required$]],\backslash$table$[[$Probability of$],[$Being in Stock$]],\backslash$table$[[$Probability of$],[$Stockout$]]],[1,84\mathrm{.}13\%,15\mathrm{.}77\%$Freeport Corporation finds that average demand for surfboards is $10$ units per day, with a standard deviation of $3$ units. Lead time from the supplier averages $12$ days, with a standard deviation of $2$ days. The item costs $$50$ and the inventory carrying cost is $30$ percent. Use Table $7-2.$

What is the standard deviation of demand during lead time for this problem?

Suppose management decides to offer a $95$ percent service level; that is$,$ it is willing to experience a stockout probability of $5$ percent during the order cycle. How much safety stock should be carried?

How much is the annual inventory carrying cost of the safety stock because of this decision?

You decide that you want this company to give better service to its customers. You decide that a $99$ percent service level is appropriate. How much safety stock must be carried to offer this service level?

What is the additional inventory carrying cost that will be incurred on this item because of your decision to increase the service level?

What will the reorder point be for the company if your decision is implemented?