There is no way to know except to try. It is very dependent on the building and the uses.
When you say "150 ft out to our shop," it conjures up the idea of a metal or concrete block walled building. It is unlikely that usable wifi will work at 150 feet through those walls. Also range extenders typically cut the speed of the wifi in half to get the job done. If this is for business use and you don't want to play around, try using a wired outdoor access point from Engenius. They are in both directional (to get the longest range coverage) and omni directional (to cover a circular area from the point) depending on your needs. They have the advantage of using power over ethernet so there is no need for an electrical outlet at the...