We want the integral of the standard normal from -z to z to be 0.85. Let's look at some standard normal tables and pick the right one.
It's easy to find the Erf one, which is the integral of the unit normal from 0 to z. That will be exactly half of the integral from -z to z. So we look for the z value corresponding to a probability of 0.425 in that table and find
z = 1.44
Answer: 1.44
[figure from Wikipedia]