The mean is 18.1

• The z-score for 13.0 is - 1.7

What is the standard deviation for this data set?

The standard deviation is 3.

The formula for a z-score is

z = (X-μ) / σ

Using our information, we have

-1.7 = (13-18.1) / σ

Multiplying both sides by σ,

-1.7σ = 13-18.1

-1.7σ = - 5.1

Divide both sides by - 1.7:

-1.7σ/-1.7 = - 5.1/-1.7

σ = 3