TABLE $13\mathrm{.}4$ The Distribution, $F(Q),$ and Expected Inventory, $/($Q$),$ Functions for a Normal Distribution with Mean $3000$ and Standard Deviation $1000$

$\backslash$table$[[z,F(z),I(z),z,F(z),I(z),z,F(z),I(z)$ Teddy Bower is an outdoor clothing and accessorles chain that purchases a line of parkas at $$8$ each from Its Aslan supplier,

TeddySports. Unfortunately, at the time of the order placement, demand is still uncertain: Teddy Bower forecasts that Its demand is

normally distributed with a mean of $1,800$ and a standard devlation of $1,300.$ Teddy Bower sells these parkas at $$23$ each. Unsold

parkas have little salvage value; Teddy Bower simply glves them away to a charity $($and also doesn't collect a tax benefit for the

donation$).$ Use Table $13\mathrm{.}4.$

Note: Do not round Intermedlate calculatlons. If a part of the questlon speclfles whether to use Table $13\mathrm{.}4,$ or to use Excel, then

credit for a correct answer will depend on using the specifled method.

a$.$ How many parkas should Teddy Bower buy from TeddySports to maximize expected profit? Use Table $13\mathrm{.}4$ and the round$-$up rule.

Note: Enter your answer as a whole number.

Order quantity

b$.$ If Teddy Bower orders $3,250$ parkas, what is expected leftover Inventory? Use Table $13\mathrm{.}4$ and the round$-$up rule.

Note: Round your answer to $2$ decimal places.

Expected leftover inventory

c$.$ If Teddy Bower orders $3,250$ parkas, what is expected sales? Use your result from Part b$.$

Note: Round your answer to $2$ decimal places.

Expected sales

d$.$ If Teddy Bower orders $3,250$ parkas, what is expected profit? Use your results from Part b and Part c$.$

Note: Round your answer to $2$ decimal places.

Expected profit

e$.$ How many parkas should Teddy Bower order to ensure a $98\mathrm{.}5\%$ In$-$stock probability? How many parkas should Teddy Bower's

order? Use Table $13\mathrm{.}4.$

Order quantity