Question

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

Answer 1

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