Question

Roberto finishes a triathlon in 63.2 minutes. Among all men in the race, the mean finishing time was 69.4 minutes with a standard deviation of 8.9 minutes. Zandra finishes the same triathlon in 79.3 minutes. Among allwomen in the race, the mean finishing time was 84.7 minutes with a standard deviation of 7.4 minutes. Who did better inrelation to their gender?

Answer 1

Answer:

Due to the lower z-score of the finishing time, Zandra was faster, that is, doing better in relation to her gender.

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

Whoever had the lower z-score was faster, that is, did better in relation to their gender.

Roberto:

63.2 minutes. Mean finishing time was 69.4 minutes with a standard deviation of 8.9 minutes. So $X = 63.2, \mu = 69.4, \sigma = 8.9$

Then

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{63.2 - 69.4}{8.9}$

$Z = -0.7$

Zandra:

79.3 minutes. Mean finishing time was 84.7 minutes with a standard deviation of 7.4 minutes. So $X = 79.3, \mu = 84.7, \sigma = 7.4$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{79.3 - 84.7}{7.4}$

$Z = -0.73$

Due to the lower z-score of the finishing time, Zandra was faster, that is, doing better in relation to her gender.