Problem $20-10($Algo$)$

You are a newsvendor selling San Pedro Times every morning. Before you get to work, you go to the printer and buy the day's paper for $\backslash (\backslash$$ $0\mathrm{.}25\backslash )$ a copy. You sell a copy of San Pedro Times for $\backslash (\backslash$$ $1\mathrm{.}00\backslash ).$ Daily demand is distributed normally with mean $\backslash (=360\backslash )$ and standard deviation $=70.$ At the end of each morning, any leftover copies are worthless and they go to a recycle bin.

a$.$ How many copies of San Pedro Times should you buy each morning? $($Use Excel's NORMSINV$()$ function to find the correct critical value for the given $\backslash ($ a $\backslash )-$level. Round your $\backslash ($ z $\backslash )-$value to $2$ decimal places and final answer to to $2$ decimal places.$)$

Optimal order quantity

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

Probability