Wood Watercolors is a commercial art gallery that uses a four-week periodic review system to reorder paintings for its showrooms. A one-week lead time is required to fill the order. Demand for one particular style of painting during the five-week replenishment period is normally distributed with a mean of 22 units and a standard deviation of 8 units.

(a)

At a particular periodic review, 12 units are in inventory. The curator places an order for 18 units. What is the probability that this style of painting will have a stock-out before an order that is placed at the next four-week review period arrives? (Round your answer to four decimal places.)

(b)

Assume that the gallery is willing to tolerate a 2.5% chance of a stock-out associated with a replenishment decision. How many paintings should the curator have ordered in part (a)? (Round your answer to the nearest integer.)

(c)

What is the replenishment level for the four-week periodic review system? (Round your answer to the nearest integer)