To find the z-score corresponding to the upper 38%, we need to consider the percentage in terms of the cumulative area from the left side of the standard normal distribution. Since we are looking for the upper 38%, the cumulative area from the left side is:

\[
1 - 0.38 = 0.62
\]

This means we want to find the z-score for which the cumulative area to the left is 0.62. We can use the standard normal distribution table (z-table) or an inverse cumulative distribution function (CDF) to find the z-score.

Looking up the cumulative probability of 0.62 in a z-table, we find that the corresponding z-score is approximately:

\[
z \approx 0.31
\]

Therefore, the z-score for the upper 38% is approximately **0.31**.

Would you like more details or explanations? Here are some related questions:

1. What is a z-score, and how is it used in statistics?
2. How do we use a z-table to find cumulative probabilities?
3. What are some applications of z-scores in real-life data analysis?
4. Can you explain the inverse cumulative distribution function in more depth?
5. How would we calculate the z-score for a lower percentile (e.g., lower 10%)?

**Tip:** Z-scores allow us to compare individual data points to the mean of a distribution by expressing how many standard deviations they are from the mean.

Learn how to calculate the z-score for the upper 38% of a standard normal distribution. This statistical problem involves understanding cumulative probability and the use of a z-table or inverse cumulative distribution function. Suitable for high school students in Grades 10-12.

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