H & K Electronic Warehouse sells a $12-$pack of AAA batteries, and this is a very popular item.

Demand for this is normally distributed, with an average of $50$ packs per day and a standard

deviation of $16.$ The average delivery time is $5$ days, with a standard deviation of $2$ days. Delivery

time has been found to be normally distributed. A $96\%$ service level is desired. $($a$)$ What is the

standard deviation of demand during the lead time? $($b$)$ How much safety stock should be carried,

and what should be the reorder point?