Please explain how to solve for a sample standard deviationwith the z-scores.

The problem I am working on is given as a sample with M = 51, x = 59 corresponds to z = 2.00.

What is the standard deviation?

I also have a distribution score of u = 78

If I have a score of x = 70 which standard deviation would give you a better grade o= 4 or o= 8?

If the score was x = 80 which standard deviation would give you the better score the o= 4 or o= 8?

How do I set this problem up to be solved?

1. We know that z = (x-M)/sd where sd is what we need to solve.

So 2.00 = (59-51)/sd, so sd = 4

2. Now x = 70 …

The solution gives detailed steps on computing standard deviation by applying standard normal formula and also comparing the z scores.