Stats: if you have two raw scores and their z scores how do you find the mean and standard deviation?

Question

This is the exact problem: For a population of exam scores, a socre of X=58 corresponds to a z- score of z= +0.50 and a score of x=46 corresponds to a z- score of z= -1.0. Find the mean and the standard deviation for the population. (hint: sketch the distribution and locate the two scores in your sketch)
So I did a sketch but still don't know how to get the answer. Please Help!!

Answer 1

The z-score is defined by z=(x-m)/s, where m is the mean and s is the standard deviation.

You have 0.5 = (58-m)/s, and -1 = (46-m)/s.

It follows from the second equation that s=m-46. Substitute that into the first equation, and you get

1/2 = (58-m)/(m-46),
or
m/2-23=58-m,
which gives
3m/2=81, or m=54.

Since s=m-46, it follows that s=8.

Answer 2

Add all of the values and divide by means of the quantity of values. This is your imply Take the change among every importance and the imply and rectangular it. Add all of those values and take the rectangular root of this sum. That is your ordinary deviation.