Question $1(35$ pts$)$: Caramel, a local coffee shop, uses on average $100$ pounds $($lbs$)$ of ground

coffee daily with a standard deviation of $20$ lbs $($assume normal distribution$).$ Nick, the store

manager, orders $1200$ lbs of ground coffee whenever the store has $427$ lbs left. Lead time with

the supplier is also normally distributed with an average of $3$ days and a standard deviation of $1$

day.

$($a$)(5$ pts$)$ What is the amount of safety stock with the current inventory policy?

$($b$)(5$ pts$)$ How many pounds of ground coffee are there in the store on average?

$($c$)(5$ pts$)$ On average, how many days does a pound of coffee sit in the store before being used?

$($d$)(10$pts$)$ What is the probability that Caramel stocks out on ground coffee with the current policy?

$($e$)(10$pts$)$ If Nick targets $2\mathrm{.}5\%$ stock$-$out probability, when should he order ground coffee from the

supplier?