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To solve for the corresponding z-score, we use the formula for the z-score:

\[
z = \frac{x - \mu}{\sigma}
\]

Where:
- \(x = 94\) (the raw score),
- \(\mu = 80\) (the mean),
- \(\sigma = 5.8\) (the standard deviation).

Substituting the values into the formula:

\[
z = \frac{94 - 80}{5.8} = \frac{14}{5.8} \approx 2.414
\]

So, the corresponding z-score is approximately \( z = 2.414 \).

Would you like more details or further clarification? Here are some related questions to explore:

1. What is the interpretation of a z-score of 2.414 in a normal distribution?
2. How would you calculate the probability associated with this z-score?
3. What is the significance of a positive vs. a negative z-score?
4. How would the z-score change if the standard deviation were larger?
5. How does the z-score relate to percentiles in a normal distribution?

**Tip:** The z-score tells you how many standard deviations a data point is from the mean.

Given a mean, standard deviation, and a raw score, find the corresponding z-score. Assume the distribution is normal. Mean 80, standard deviation 5.8, x = 94.

Learn how to calculate the z-score for a normal distribution with a mean of 80, standard deviation of 5.8, and a raw score of 94. This statistical problem demonstrates key concepts in normal distribution and z-score calculation. Suitable for high school students.

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