What Z-Score equates to the TOP 33rd percentile?

The Z-score that equates to the top 33rd percentile corresponds to the point where 33% of the data lies above it in a standard normal distribution.

To find this Z-score:

1. The cumulative probability for the bottom 67% (i.e., \(1 - 0.33 = 0.67\)) needs to be identified.
2. We use a Z-table or inverse of the standard normal distribution function.

The Z-score corresponding to a cumulative probability of 0.67 is approximately **0.44**.

Thus, the Z-score for the top 33rd percentile is **0.44**.

Would you like further details on how to calculate Z-scores, or any clarification?

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Here are 5 related questions:
1. What is a Z-score in general, and how is it interpreted?
2. How do you calculate the Z-score for any given percentile?
3. How does the Z-score relate to standard deviations from the mean?
4. Can Z-scores be negative, and what would a negative Z-score signify?
5. How can Z-scores be applied in hypothesis testing?

**Tip**: Z-scores allow you to compare data points from different distributions by normalizing them to a standard normal distribution!

Find out how to calculate the Z-score that corresponds to the top 33rd percentile in a standard normal distribution. This problem explains key statistical concepts, such as Z-scores and percentiles, using the cumulative probability function. Ideal for students in Grades 10-12.

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