etermine which score corresponds to the higher relative position.21)Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on atest with a mean of 493 and a standard deviation of 150?A)A score of 92B)Both scores have the same relative position.C)A score of 688

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**

---

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!

Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150?

Learn how to compare scores from different tests using z-scores. This problem involves calculating z-scores to determine the higher relative position of a score of 92 on a test with a mean of 71 and a standard deviation of 15, versus a score of 688 on a test with a mean of 493 and a standard deviation of 150. Suitable for students in Grades 9-12.

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