Standard Deviation Problem

I do not understand how to calculate this. I do not think that there is enough information. I think I need at a minimum, the mean or the students scores, but this is all that was provided.

On a certain statistics exam, two examinees had z?scores that differed by 2.0 points and had raw
scores that differed by 20 points. What is the standard deviation of these raw scores?

Yes, there is enough info.

If you set up two equations:

\(\displaystyle z=\frac{x-{\mu}}{s}\) and \(\displaystyle z+2=\frac{(x+20)-{\mu}}{s}\)

You can solver for s and get a definitive solution.

Solve \(\displaystyle \frac{x-{\mu}}{s}+2=\frac{(x+20)-{\mu}}{s}\) for s and you have it.

Provided I pick any random number for x I.E. 80, I still do not know mue. I still have two unknowns.

No, you don't. They cancel out and you can solve for an exact value of s.

Solve the last equation I gave for s.