The time it takes runners to complete a certain marathon are normally distributed with a mean of 4.6 hours and a standard deviation of 1.1 hours

What is the time for a runner with a z-score of - 1.2

Round to the nearest hundredth

The time for this z-score is 3.28.

The formula for z-scores is

z = (X-μ) / σ

Using our information, we have

-1.2 = (X-4.6) / 1.1

Multiply both sides by 1.1:

-1.2 (1.1) = X - 4.6

-1.32 = X - 4.6

Add 4.6 to both sides:

-1.32 + 4.6 = X - 4.6 + 4.6

3.28 = X