Question

The times 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 ?

Enter your answer, rounded to the nearest hundredth, in the box.

Answer 1

Answer: 3.28 hours

Step-by-step explanation:

Since the times it takes runners to complete a certain marathon are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = time for a runner.

µ = mean time

σ = standard deviation

From the information given,

µ = 4.6 hours

σ = 1.1 hours

The z-score is - 1.2

Therefore,

- 1.2 = (x - 4.6)/1.1

Cross multiplying by 1.1, it becomes

1.1 × - 1.2 = x - 4.6

- 1.32 = x - 4.6

x = - 1.32 + 4.6

x = 3.28 hours to the nearest hundredth