\( Z_{0.64} \) refers to the Z-score in a standard normal distribution corresponding to a cumulative probability of 0.64. To find \( Z_{0.64} \), we look for the Z-score where the area to the left under the standard normal curve is 0.64.

Using standard Z-tables or a calculator, the Z-score corresponding to a cumulative probability of 0.64 is approximately:

\[
Z_{0.64} \approx 0.36
\]

This means that 64% of the data lies below a Z-score of 0.36 in a standard normal distribution.

Would you like further clarification, or do you have any questions?

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Here are 5 related questions:
1. What is the interpretation of a Z-score in statistics?
2. How can you calculate the probability for any Z-score using Z-tables?
3. What is the Z-score for a cumulative probability of 0.75?
4. How do you convert a raw score to a Z-score in a normal distribution?
5. How do you find cumulative probabilities for negative Z-scores?

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

Understand how to find the Z-score for a cumulative probability of 0.64 using the standard normal distribution. This detailed solution shows that Z0.64 is approximately 0.36, covering key concepts like Z-scores, cumulative probability, and the 68-95-99.7 rule. Ideal for students in Grades 10-12.

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