A retailer uses a periodic review inventory model. The daily demand for the product in question is normally distributed with a mean of $45$and a standard deviation of $16.$Currently it places orders every two weeks, and the shipment lead time is four days. The retailer has a $96\mathrm{.}5\%$ service policy.

$1-$ What is the required inventory the manager should aim to order every time they place an order?

$2-$ What should the order amount be if the current inventory is $175$ units?