Question

Marcus runs a half-marathon in 98 minutes and a marathon in 225 minutes. The half-marathon times are normally distributed with a mean of 105 minutes and a standard deviation of 14 minutes. The marathon times are normally distributed with a mean of 235 minutes with a standard deviation of 30 minutes. In terms of relative position, at which distance is he a better runner?

Answer 1

Solution :

Given that ,

Using z-score formula,

z = x - /   

z = 98 - 105 / 14

z = -0.50 ( half marathon)

Using z-score formula,

z = x - /   

z = 225 - 235 / 30

z = -0.33 ( marathon)

marathon distance is he a better runner, because marathon z-score -0.33 is larger than half marathon z-score -0.50.