To solve for \( z \) in the equation \( P(Z < z) = 0.9500 \), we need to look up the z-score that corresponds to a cumulative probability of 0.9500 in the standard normal distribution.

### Steps:
1. **Standard Normal Distribution (Z-Distribution):** The cumulative probability function gives the probability that a standard normal random variable \( Z \) is less than a particular value \( z \). 
2. **Using Z-Tables or a Calculator:** From standard z-tables or using a statistical calculator, we can find the z-score that corresponds to a cumulative probability of 0.9500.

The z-score that corresponds to \( P(Z < z) = 0.9500 \) is approximately **1.645**.

This means that for a standard normal distribution, 95% of the data lies below \( z = 1.645 \).

### Summary:
- \( z = 1.645 \) for \( P(Z < z) = 0.9500 \).

Would you like more details on how to read z-tables or have any other questions?

Here are some related questions:
1. What is the z-score for \( P(Z < z) = 0.9750 \)?
2. How do you calculate probabilities using the standard normal distribution?
3. What is the probability for \( P(Z < z) \) when \( z = 1.96 \)?
4. How do you find the z-score for a given cumulative probability using technology?
5. What is the significance of z-scores in hypothesis testing?

**Tip:** Z-tables are often cumulative from the left, meaning they show the probability from \( Z = -\infty \) to a given z-value.

Discover how to find the z-score for a cumulative probability of 0.9500 in the standard normal distribution. This problem covers core probability concepts, including z-scores and the standard normal distribution. Suitable for students in Grades 10-12.

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