Use Table $14\mathrm{.}1.$ ACold Incorporated is a frozen$-$food distributor with $10$ warehouses across the country. Ivan Tory, one of the warehouse managers, wants to make sure that the inventory policies used by the warehouse are minimizing inventory while still maintaining quick delivery to ACold$$s customers. Because the warehouse carries hundreds of different products, Ivan decided to study one. He picked Caruso$$s Frozen Pizza $($CFP$).$ Demand for CFPs averages $387$ per day with a standard deviation of $156.$ Because ACold orders at least one truck from its supplier each day, ACold can essentially order any quantity of CFP it wants each day. In fact, ACold$$s computer system is designed to implement an order$-$up$-$to policy for each product. Ivan notes that any order for CFPs arrives five days after the order.

$1.$ Suppose an order$-$up$-$to level of $2,412$ is used. What is the expected on$-$hand inventory?

Note: Use Table $14\mathrm{.}1$ and round to nearest integer.

$2.$ Suppose an order$-$up$-$to level of $1,933$ is used. What is the in$-$stock probability?

Note: Use Table $14\mathrm{.}1.$ Round your answer to $1$ decimal.

Table $14\mathrm{.}1$ :

The Distribution Function, F$($z$),$ and the Inventory I$($Z$),$ for the Standard Normal Distribution Function, show below:

Z F$($Z$)$ I$($Z$)$

$-4\mathrm{.}00\mathrm{.}00000\mathrm{.}0000$

$-3\mathrm{.}90\mathrm{.}00000\mathrm{.}0000$

$-3\mathrm{.}80\mathrm{.}00010\mathrm{.}0000$

$-3\mathrm{.}70\mathrm{.}00010\mathrm{.}0000$

$-3\mathrm{.}60\mathrm{.}00020\mathrm{.}0000$

$-3\mathrm{.}50\mathrm{.}00020\mathrm{.}0001$

$-3\mathrm{.}40\mathrm{.}00030\mathrm{.}0001$

$-3\mathrm{.}30\mathrm{.}00050\mathrm{.}0001$

$-3\mathrm{.}20\mathrm{.}00070\mathrm{.}0002$

$-3\mathrm{.}10\mathrm{.}00100\mathrm{.}0003$

$-3\mathrm{.}00\mathrm{.}00130\mathrm{.}0004$

$-2\mathrm{.}90\mathrm{.}00190\mathrm{.}0005$

$-2\mathrm{.}80\mathrm{.}00260\mathrm{.}0008$

$-2\mathrm{.}70\mathrm{.}00350\mathrm{.}0011$

$-2\mathrm{.}60\mathrm{.}00470\mathrm{.}0015$

$-2\mathrm{.}50\mathrm{.}00620\mathrm{.}0020$

$-2\mathrm{.}40\mathrm{.}00820\mathrm{.}0027$

$-2\mathrm{.}30\mathrm{.}01070\mathrm{.}0037$

$-2\mathrm{.}20\mathrm{.}01390\mathrm{.}0049$

$-2\mathrm{.}10\mathrm{.}01790\mathrm{.}0065$

$-2\mathrm{.}00\mathrm{.}02280\mathrm{.}0085$

$-1\mathrm{.}90\mathrm{.}02870\mathrm{.}0111$

$-1\mathrm{.}80\mathrm{.}03590\mathrm{.}0143$

$-1\mathrm{.}70\mathrm{.}04460\mathrm{.}0183$

$-1\mathrm{.}60\mathrm{.}05480\mathrm{.}0232$

$-1\mathrm{.}50\mathrm{.}06680\mathrm{.}0293$

$-1\mathrm{.}40\mathrm{.}08080\mathrm{.}0367$

$-1\mathrm{.}30\mathrm{.}09680\mathrm{.}0455$

$-1\mathrm{.}20\mathrm{.}11510\mathrm{.}0561$

$-1\mathrm{.}10\mathrm{.}13570\mathrm{.}0686$

$-1\mathrm{.}00\mathrm{.}15870\mathrm{.}0833$

$-0\mathrm{.}90\mathrm{.}18410\mathrm{.}1004$

$-0\mathrm{.}80\mathrm{.}21190\mathrm{.}1202$

$-0\mathrm{.}70\mathrm{.}24200\mathrm{.}1429$

$-0\mathrm{.}60\mathrm{.}27430\mathrm{.}1687$

$-0\mathrm{.}50\mathrm{.}30850\mathrm{.}1978$

$-0\mathrm{.}40\mathrm{.}34460\mathrm{.}2304$

$-0\mathrm{.}30\mathrm{.}38210\mathrm{.}2668$

$-0\mathrm{.}20\mathrm{.}42070\mathrm{.}3069$

$-0\mathrm{.}10\mathrm{.}46020\mathrm{.}3509$

$0\mathrm{.}00\mathrm{.}50000\mathrm{.}3989$

$0\mathrm{.}10\mathrm{.}53980\mathrm{.}4509$

$0\mathrm{.}20\mathrm{.}57930\mathrm{.}5069$

$0\mathrm{.}30\mathrm{.}61790\mathrm{.}5668$

$0\mathrm{.}40\mathrm{.}65540\mathrm{.}6304$

$0\mathrm{.}50\mathrm{.}69150\mathrm{.}6978$

$0\mathrm{.}60\mathrm{.}72570\mathrm{.}7687$

$0\mathrm{.}70\mathrm{.}75800\mathrm{.}8429$

$0\mathrm{.}80\mathrm{.}78810\mathrm{.}9202$

$0\mathrm{.}90\mathrm{.}81591\mathrm{.}0004$

$1\mathrm{.}00\mathrm{.}84131\mathrm{.}0833$

$1\mathrm{.}10\mathrm{.}86431\mathrm{.}1686$

$1\mathrm{.}20\mathrm{.}88491\mathrm{.}2561$