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 score of -1.2? Round to the nearest hundredth

Answer 1

The answer is 3.28.

Explanation:

The formula for a z-score is 
z = (X-μ)/σ,

where μ is the mean and σ is the standard deviation.

For our problem, we know that z = -1.2, μ = 4.6 and σ = 1.1:

-1.2 = (X-4.6)/1.1

Multiply both sides by 1.1:

-1.2(1.1) = ((X-4.6)/1.1)*1.1
-1.32 = X-4.6

Add 4.6 to both sides:
-1.32+4.6 = X-4.6+4.6
3.28 = X

Answer 2

The equation for the z-score is  

z-Score = (Time - Mean) / Standard Deviation
Given:
mean = 4.6 hours
standard deviation = 1.1 hours
z-Score = -1.2
 ∴ -1.2 = (x - 4.6) / 1.1
  x - 4.6 = -1.32
  x = 3.28 hours

The time would be 3.28 hours for a z-score of -1.2.