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To swimmers Angie aTwo swimmers Angie and Beth from different states wanted to find out who had the fastest time for the 50 m freestyle when compared to her team which swimmer had the fastest time when compared to her team

Sagot :

Using z-scores, it is found that due to the lower z-score, Beth had the fastest time when compared to her team.

What is the missing information?

This problem is incomplete, but researching on the internet, we have that:

  • Angie had a time of 26.2 seconds, while her team had a mean time of 27.2 seconds with a standard deviation of 0.8 seconds.
  • Beth had a time of 27.3 seconds, while her team had a mean time of 30.1 seconds with a standard deviation of 1.4 seconds.

What are z-scores?

The z-score of a measure X in a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

For this problem, lower times means that the swimmer is faster, hence the swimmer that had the fastest time when compared to her team is the swimmer with the lowest z-score.

Angie's z-score is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (26.2 - 27.2)/0.8

Z = -1.25.

Beth's z-score is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (27.3 - 30.1)/1.4

Z = -2.

Due to the lower z-score, Beth had the fastest time when compared to her team.

More can be learned about z-scores at https://brainly.com/question/24537145

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