I recently purchased a large quantity of commercially manufactured jacketed bullets (major named high end company) The bullets were supposed to be 160 grains weight.  7% were more than .5 grain light and 2% were more than .5 grain heavy. Extreme spread over 1.5 grains.  I screened for plus or minus .15 grains and almost 56% made the cut. Is this the norm? Am I being too picky? Will that spread really make any difference in accuracy?

There are a few manufacturers that DO care about their products.   

A few decades ago I got a CALL from Jim Berger because I asked a simple question on a postcard.  I was and AM impressed.  We had a very interesting conversation about quality.

A phone call from you to their quality assurance (whom ever the company is) might be enlightening.