Inquiry $1$: The Plant Manager $($PM$)$ comes to your office and shuts your office door. The plant manager says $"$T have been out of college for some time, now. Since you graduated more recently than me $($the PM chuckles$),$ I hope you can help me understand how corporate headquarters determined we need to order $713$ pounds of coffee for our Mount Olive location ${?}^{20}[$the PM hands you a piece of paper with the information and figures on it $($below$).$ Note, too, that the PM has included some very important notes about MS Excel $($below$)].$ The PM continues: "Please show all your work so I can make sure you have not missed anything $($the PM chuckles$)!$ Here is all the information I have from corporate headquarters and some notes that I have included from my college days."

Piece of paper with information, figures, and important notes $($continued on next page$)---$

Moonbux orders all its coffee to be shipped directly from South America. A US$-$based distributor stops by every four weeks to take orders for the Mount Olive location. Because the orders are shipped directly from South America, they talke three weeks to arrive.

Moonbux Mount Olive location uses an average of $150$ pounds of coffee each week, with a standard deviation of $30$ pounds. Mroonbus prides itself on offering only the best$-$quality ingredients with a high level of service, so it wants to ensure a $98\mathrm{.}0\%$ probability of not stocking out on coffee.

Assume that the sales representative just walked in the door and there are currently $500$ pounds of coffee in the temperature and humiditycontrolled storage area. How many pounds of coffee would you order?

PMPs notes $($hints that may be very useful$)$:

Use Excel's NORMS INV$($ function to find the $z$ value.

Do not round intermediate calculations. Round $z$ value to $2$ decimal places and final answer to the nearest whole number.

$z$ value $=$ NORM. INV $($probabilit$)$; in Excel enter $"=$NORMS.INV $($probabilit$)$ where probability is the probability of not stocking out

$q=d{b}_{ar}^{**}(T+L)+z^{**}{}_{\text{T}\text{i}\text{z}}-$I