Question

A set of data has a mean of 12 and a standard deviation of 3. A data point of the set has a z-score of 1.3. What does a z-score of 1.3 mean?

Answer 1

A z-score tells you how many standard deviations a point is from the mean.
$z = \frac{x - mean}{std dev}$
Working backwards with this formula,
$x = z*std dev + mean \\ \\ x = 1.3*3 + 12 \\ \\ x = 15.9$

So the data point is 15.9 and is 1.3 std deviations from the mean of 12.

Hope this helps.