David A. answered • 10/12/22
Experienced Python programmer; Effective SAT prep tutor; Mentor
The z-score of a data point comes from the probability distribution. It basically tells you how far away the point is from the mean in units of standard deviation. About 68% of all the data will have a z-score in between -1 and +1.
The formula to calculate z-score is z = (x - mean) / σ, where x is some data point.
In the problem you provided, (x - mean) is given to you: a score (let's call it 's') 4 points above the mean will make the quantity (s - mean) = 4, because we know s is 4 more than the mean. So all that is left for you to do is divide this by the standard deviation to get your answer.
Hope this helps! Feel free to reach out if you are still having difficulty understanding.
