Standard Deviation Problem

[brew32]

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?

 

[galactus]

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.

 

[brew32]

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

 

[galactus]

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.