AQ$3.$ Inventory Management $(10$ marks$)$

A retail store needs to determine the optimal ordering policy for a kind of carbonated drinks. The lead time is $2$ weeks. Weekly demand is normally distributed with a mean of $200$ bottles and a standard deviation of $20$ bottles.$$

$1.[6$ marks$]$ In order to achieve a $95\%$ service level, how many bottles of carbonated drinks should the store keep as the safety stock? And at what inventory level should the store start placing an order?$$

$2.[4$ marks$]$ What service level can be achieved if the store always starts placing an order when the number of bottles drops to $424$ bottles?