To find the percentage of all values in a normal distribution for the given z-score (where $z \geq 1.52$), we'll follow these steps:

Step 1: Find the cumulative probability for $z = 1.52$

Using the standard normal distribution table or a calculator, we find the cumulative probability (area to the left) for $z = 1.52$.

The cumulative probability $P(Z < 1.52)$ is approximately 0.9357.

Step 2: Calculate the area to the right

Since we want the area to the right of $z = 1.52$, we subtract the cumulative probability from 1:

$P(Z \geq 1.52) = 1 - P(Z < 1.52) = 1 - 0.9357 = 0.0643$

Step 3: Convert to a percentage

To convert this to a percentage, multiply by 100:

$P(Z \geq 1.52) = 0.0643 \times 100 = 6.43\%$

Final Answer:

Approximately 6.43% of the values in a normal distribution have a z-score greater than or equal to 1.52.

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Would you like further details on how the standard normal distribution table works, or do you have any other questions?

Here are 5 related questions you might find interesting:

1. What is the percentage for a z-score less than or equal to 1.52?
2. How would you find the percentage for $z \geq 2.33$?
3. Can you calculate the percentage for a z-score between two values, such as $1.52$ and $2.33$?
4. What is the area under the curve for the entire normal distribution?
5. How is the z-score related to standard deviation in a normal distribution?

Tip: When working with normal distributions, remember that the total area under the curve is always 1 (or 100%). This means you can use the cumulative probabilities and symmetry properties to find areas in any section of the distribution.