$$AQ$3.$ Inventory Management $(12$ marks$)$

Regional Supermarket is open all year round. Daily use of cash register tapes average $36$ rolls. Usage appears normally distributed with a standard deviation of $6\mathrm{.}2$ rolls per day.$$

$1.[6$ marks$]$ If lead time is $5$ days, what reorder point should be used to achieve a target service level of $92\%?$

$2.[6$ marks$]$ Suppose that lead time is normally distributed with mean $4\mathrm{.}8$ days and standard deviation of $0\mathrm{.}9$ days. What is the service level if the reorder point is $240$ rolls?