AQ$3.$ Inventory Management $(12$ marks$)$ A manufacturing company produces and sells a high$-$tech component that is used in the aerospace industry. The monthly demand has a mean of $800$ units and a standard deviation of $100$ units. One month has $20$ working days. Note: The following two questions are independent of each other.

$1.[6$ marks$]$ If lead time is $12$ working days, what reorder point should be used to achieve a target service level of $94\%?$

$2.[6$ marks$]$ Suppose that lead time is normally distributed with a mean of $10$ days and a standard deviation of LT days. When the reorder point is $560$ units, the service level is $82\%.$ What is the standard deviation of lead time LT $($in days$)?$