PA $13-5($Algo$)$ Teddy Bower is an outdoor clothing and accessorles chaln...

Teddy Bower is an outdoor clothing and accessorles chain that purchases a line of parkas at $$12$ each from its Aslan suppller,

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 $2,200$ and a standard deviation of $1,500.$ Teddy Bower sells these parkas at $$18$ each. Unsold

parkas have little salvage value; Teddy Bower simply gives 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 intermediate calculations. If a part of the question specifies whether to use Table $13\mathrm{.}4,$ or to use Excel, then

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

a$.$ What is the probability this parka turns out to be a "dog", defined as a product that sells less than half of the forecast? Use Excel.

Note: Round your answer to $4$ decimal places.

b$.$ 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.

c$.$ If Teddy Bower orders $2,500$ parkas, what is the In$-$stock probability? Use Excel.

Note: Round your answer to $4$ decimal places.

d$.$ If Teddy Bower orders $2,500$ parkas, what is expected leftover Inventory? Use Table $13\mathrm{.}4$ and the round$-$up rule.

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

e$.$ If Teddy Bower orders $2,500$ parkas, what is expected sales? Use your result from Part d$.$

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

f$.$ If Teddy Bower orders $2,500$ parkas, what is expected profit? Use your results from Part $d$ and Part e$.$

TABLE $13\mathrm{.}4$ The Distribution, $)$