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.