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

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: 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.

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.

How many parkas should Teddy Bower buy from TeddySports to maximize expected profit? Use Table $13\mathrm{.}4.$

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

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

If Teddy Bower orders $2,500$ parkas, what is expected leftover inventory? Use Excel.

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

If Teddy Bower orders $2,500$ parkas, what is expected sales? Use Excel.

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

If Teddy Bower orders $2,500$ parkas, what is expected profit? Use Excel.

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

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 $13\mathrm{.}4.$