Question

Which of the following fitness scores is the highest relative score?

a score of 39 on a test with a mean of 31 and a standard deviation of 6.1

a score of 1136 on a test with a mean of 1080 and a standard deviation of 67.8

a score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5

All scores are relatively equal.

Answer 1

Due to the higher z-score, the correct option regarding the highest relative score is:

A score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5.

What is the z-score formula?

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean, hence the higher the z-score, the higher the score X is relative to other scores.

The respective z-scores for this problem are given by:

• (39 - 31)/6.1 = 1.31.

• (1136 - 1080)/67.8 = 0.83.

• (4730 - 3960)/555.5 = 1.39.

Hence the correct option is:

A score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5.

More can be learned about z-scores at https://brainly.com/question/28096232

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