Finding z score

Question

 A distribution has a standard deviation of σ=12. Find the z=score for the following locations in the distribution.

Above the mean by 3 points.

Above the mean by 12 points.

Below the mean by 24 points.

Below the mean by 18 points.

Answer 1

Let m = mean.  Then z = z-score of a data point = [data point - mean]/(standard deviation]

 

If data point = m+3, then z = [(m+3) - m]/12 = 0.25

 

If data point = m+12, then z = [(m+12) - m]/12 = 1

 

If data point = m-24, then z = [(m-24) - m]/12 = -2

 

I'll let you try the last one.