Question

1. neils best time in the half marathon is 139.4 minutes, while his best time in the full marathon is 222 minutes. the mean time to complete the half marathon is 117 minutes with a standard deviation of 4 minutes among world class runners, and the mean time to complete the full marathon is 212 minutes with a standard deviation of 4 minutes among world class runners. 9a what is the z - score of neils best time in the half marathon? $z_{half} = $

Explanation:

Step1: Recall z-score formula

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $x$ is the individual value, $\mu$ is the population mean, and $\sigma$ is the population standard deviation.

Step2: Identify given values

For the half marathon: $x = 139.4$ minutes, $\mu = 117$ minutes, $\sigma = 4$ minutes.

Step3: Substitute values into formula

$z_{\text{half}} = \frac{139.4 - 117}{4}$

Step4: Calculate numerator first

$139.4 - 117 = 22.4$

Step5: Compute final z-score

$\frac{22.4}{4} = 5.6$

Answer:

5.6