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 neil’s best time in the half marathon? \\( z_{half} = 5.6 \\) 9b what is the z - score of neil’s best time in the full marathon? \\( z_{full} = \\) enter your next step here

Explanation:

Step1: Recall z-score formula

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

Step2: Identify values for full marathon

For Neil's full marathon time: $x = 222$ minutes, $\mu = 212$ minutes, $\sigma = 4$ minutes.

Step3: Substitute values into formula

$z_{full} = \frac{222 - 212}{4}$

Step4: Calculate the result

$z_{full} = \frac{10}{4} = 2.5$

Answer:

$z_{full} = 2.5$