A distributor of computer monitors purchases the monitors from an overseas

supplier under a continuous review system. The average demand for a popular

computer monitor is normally distributed with a mean of $50$ units a day and a

standard deviation of $10$ units a day. It costs $$75$ to process each order and

there is a $16$ day lead time. The holding cost for each monitor is $$20$ per year

and the distributor wishes to maintain a $90\%$ service level. The distributor

operates $300$ days in a year.

What is the standard deviation of demand throughout the sixteen$-$day lead$-$time

period?

$40$ units

$65$ units

$160$ units

$100$ units