Every year, Ms$.$ Smith needs to order Christmas trees in Sep. for sales in Dec. in her convenient

store. Ms$.$ Smith has only one chance to order, she can't order more after the tree growing

season.

In the selling season from $10$ to $24$ Dec, she sells a tree for $$55.$

It costs her $$25$ each to order now.

On $25$ Dec, she can sell a tree with huge discount for $$30$

After $25$ Dec, she salvages the extra trees for $$10$ each.

The demand for the regular period can be described as a normal distribution with mean $32$ trees

and standard deviation $4$ trees

The demand on Dec $25$ follows uniform distribution with min and max $0$ and $5,$ respectively

How many trees should Ms$.$ Smith order? Hint: You can try an order of $28,32,36$ and $40$ and

report the average and confidence interval. Assume $n=500.$