To determine which score has the higher relative position, we can use z-scores. The z-score measures how many standard deviations a data point is from the mean. It is calculated using the formula:

$z = \frac{x - \mu}{\sigma}$

Where:

• $x$ is the score,
• $\mu$ is the mean,
• $\sigma$ is the standard deviation.

First Test (Score of 92):

• Mean ($\mu$) = 71
• Standard deviation ($\sigma$) = 15
• Score ($x$) = 92

The z-score is:

$z_1 = \frac{92 - 71}{15} = \frac{21}{15} = 1.4$

Second Test (Score of 688):

• Mean ($\mu$) = 493
• Standard deviation ($\sigma$) = 150
• Score ($x$) = 688

The z-score is:

$z_2 = \frac{688 - 493}{150} = \frac{195}{150} = 1.3$

Conclusion:

• The z-score for the first test is 1.4.
• The z-score for the second test is 1.3.

Since 1.4 > 1.3, a score of 92 on the first test corresponds to a higher relative position.

Thus, the answer is: A) A score of 92

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Would you like more details on z-scores or any other clarification?

Here are 5 related questions for further learning:

1. How do z-scores relate to percentiles in a normal distribution?
2. Can z-scores be negative, and what do they represent?
3. How can you use z-scores to compare scores from different distributions?
4. What is the empirical rule and how does it relate to standard deviations?
5. How can you calculate probabilities using z-scores?

Tip: When comparing scores from different distributions, always standardize them using z-scores to get meaningful comparisons!