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The problem asks for the probability associated with a standard normal distribution \( z \) corresponding to a specific region on the curve, marked at \( z = -0.45 \).

To find this probability, we need to look up the cumulative probability for \( z = -0.45 \) in the standard normal distribution table (Z-table). The Z-table gives the area under the standard normal curve to the left of a given z-value.

1. For \( z = -0.45 \), the cumulative probability from the Z-table is approximately **0.3264**.

This means the area to the left of \( z = -0.45 \) is 0.3264, which is the required probability. Thus, the probability of \( z \) occurring in the shaded region is approximately **0.3264**.

Would you like further details on how to use the Z-table or the steps to verify this? Feel free to ask any questions!

Here are some related questions to deepen your understanding:
1. How do you interpret the area under the curve in a standard normal distribution?
2. What is the total area under the standard normal distribution curve?
3. How would you calculate the probability for a positive z-value, such as \( z = 0.45 \)?
4. How can we find the probability between two z-values, like between \( z = -0.45 \) and \( z = 0.45 \)?
5. What happens to the probability if \( z \)-values increase or decrease significantly?

**Tip**: When using the Z-table, always remember that it provides cumulative probabilities from the left of the curve to your chosen z-value.

For the standard normal distribution shown on the right, find the probability of z occurring in the indicated region (z = -0.45).

This guide explains how to find the probability associated with a z-score of -0.45 in a standard normal distribution. Using the Z-table, we calculate the area under the curve to determine the probability, which is approximately 0.3264. Learn more about probability theory and normal distribution concepts.

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