The amount of DNA that is associated with each nucleosome is a approximately 200 bp. This is determined by treating chromatin wwith a certain enzyme that cuts DNA. This enzyme is called DNases. Every chromosome has hundred of thousands of nucleosomes that are joined by DNA strands that pass between them.
A nucleosome is a structure that is consists of DNA wrapped around 8 sub-units of a protein namely the histone protein. There are packing of these materials around the proteins decide the transcription site of most of the RNA.
The amount of DNA that is packaged inbetween is about 1.7 turns of the DNA that contains 146 base pairs and about 20 base pairs are in between the turns which sums it to 166 base pairs associated with each nucleosome.