The manager of a grocery store reviews inventory of a particular brand of dishwasher soap every $25$ days.

The supplier of the dishwasher soap delivers the orders placed by the store in $5$ days.

The daily demand for the dishwasher soap is approximately normal with a mean of $12$ bottles per day and a daily standard deviation of $3$ bottles.

The desired service level for this shampoo is $95\%.$

$1.$ What is the target inventory level?

$2.$ What is the average amount of safety stock?

$3.$ If the amount of dishwasher soap on hand at reorder time is $42$ bottles, what should the order quantity be$?$