Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $$12$ each from its Asian 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 deviation of $1,300.$ Teddy Bower sells these parkas at $$19$ 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$)$ How many parkas should Teddy Bower buy from TeddySports to maximize expected profit? Use Table $13\mathrm{.}4$ and the round$-$up rule.

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

c$)$ If Teddy Bower orders $2,500$ parkas, what is expected sales? Use your result from Part b

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

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 $13\mathrm{.}4.$

Please show steps and show what is the answer clearlly.