As a newspaper distributor in Chicago, you are attempting to minimize oversupply to maximize profits. When you purchase the newspapers from the printer, you buy the day$$s paper for $$0\mathrm{.}25$ a copy. You sell a copy of the paper for $$1\mathrm{.}00.$ Daily demand is distributed normally with mean $=250$ and standard deviation $=25.$ At the end of each morning, any leftover copies are worthless and they go to a recycle bin.

a$.$ How many copies of the newspaper should you buy each morning? $($Use Excel's NORMSINV$()$ function to find the Z$-$score. Round intermediate calculations to four decimal places. Round your answer to the nearest whole number.$)$

Optimal order quantity

b$.$ Based on part $($a$)$ above, what is the probability that you will run out of stock? $($Round your answer to the nearest whole percent.$)$

Probability

$\%$