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.