Daily demand for a product is $200$ units, with a standard deviation of $35$ units. The review period is $20$ days and the lead time is $6$ days. At the time of review, there are $20$ units in stock.

If $90$ percent service probability is desired, how many units should be ordered?

Note: Use Excel's NORM.S$.$INV$()$ function to find the z value. Round z value to $2$ decimal places and final answer to the nearest whole number.