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The problem involves finding the area under the standard normal curve for a \( z \)-score of 0.73. The area you're looking for corresponds to the cumulative probability from \( z = -\infty \) to \( z = 0.73 \), which represents the shaded region under the curve.

We can use a standard normal distribution table (or calculator) to find the cumulative area corresponding to a \( z \)-score of 0.73.

Looking up \( z = 0.73 \) in the standard normal table:

- The cumulative probability (area) is approximately **0.7673**.

Thus, the area of the shaded region is approximately **0.7673** (rounded to four decimal places).

Would you like more details or have any further questions?

Here are five related questions to consider:
1. How do you find the area under the standard normal curve for negative \( z \)-scores?
2. What does the area under the standard normal curve represent in terms of probability?
3. How can you calculate areas for more complex \( z \)-score ranges?
4. How is the \( z \)-score calculated in a normal distribution with different means and standard deviations?
5. How do we interpret the area found in real-world applications?

**Tip**: When working with standard normal distributions, remember that areas to the left of a \( z \)-score are cumulative probabilities, and you can use symmetry for negative \( z \)-scores.

Find the area of the shaded region for a standard normal distribution where z = 0.73.

Calculate the area of the shaded region for a standard normal distribution with a z-score of 0.73. This problem explores key statistical concepts such as z-scores and the standard normal distribution. The area, or cumulative probability, is found using standard z-tables or statistical software.

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