Answer and Explanation:
The average distance between restriction sites refers to how frequently the restriction endonuclease with the recognition sequence ACGT might cut the double-stranded DNA.
We know that the frequency of cutting in a determined DNA sequence is (1/4)ⁿ, n being the number of bases in the recognition sequence, and 4 being the number of possible nucleotides.
So, in the present example, the restriction endonuclease recognizes the sequence ACGT, formed by 4 bases. This is, n=4.
The frequency of the ACGT sequence is (1/4)⁴= 1/256. The enzyme cuts every 256 bases. The average distance between restriction sites 0.25 kb.
Note: This is for only one of the strands of DNA.