the area under the distribution curve is telling you the probability that you will have a z-score less than the indicated z-score.
if you want the probability that you will have a z-score greater than the indicated z-score, you would have to subtract the area shown from 1.
that gives you the area under the distribution curve greater than the indicated z-score.
that's the same as telling you the probability that you will have a z-score greater than the indicated z-score.
your problem states:
p (z > k) = .85
k is the indicated z-score.
this formula is telling you that the probability that your z-score (z) is greater than the indicated z-score (k) is .85.
since the z-score tells you the probability that your z-score is less than the indicated z-score, you want to find the z-score that has 1 - .85 = .15 to the left of it.
i looked in the z-score table and found that a z-score of -1.3 has an area to the left of it under the distribution curve of .1515.
this means the area to the right of it is 1 - .1515 = .8485
i also found that a z-score of -1.4 has an area to the left of it under the distribution curve of .1492.
this means the area to the right of it is 1 - .1492 = .8508
since i want greater than .85 to the right of it, i chose a z-score of -1.4.
the z-score table i used can be found here.
http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf
if you use a z-score calculator, you could get more exact.
using my ti-84 calculator, i calculated a z-score of -1.03643338
this is generally a lot more accuracy than you need, so i rounded it to -1.0364.
if you rounded this to 2 decimal digits, it would be -1.04, as shown in the z-score table.
there is a neat little z-score calculator online that actually shows you the distribution curve as well as gives you the answer.
that z-score calculator can be found here.
http://davidmlane.com/hyperstat/z_table.html
with this calculator, i just told it the area to the right of the z-score and it told me the z-score.
the display of what i did is shown below:
the shaded area to the right of the z-score is the area under the normal distribution curve that is the right of the indicated z-score.
the indicated z-score is -1.36.
you could have interpolated this value from the z-score table but, in most cases, it's not necessary.
there are other z-score calculators online but this one is one of the best out there because it shows you what's going on as well as giving you the answer plus it's extremely easy to use.