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The question is asking to find the area of the shaded region, which is the cumulative probability up to the given z-score of \( z = -0.85 \) on a standard normal distribution (with mean \( \mu = 0 \) and standard deviation \( \sigma = 1 \)).

To find the area under the curve for a standard normal distribution, you can use a z-table or a calculator. The area to the left of \( z = -0.85 \) is the cumulative probability.

1. From the z-table, look up the value corresponding to \( z = -0.85 \).
2. The cumulative probability for \( z = -0.85 \) is approximately **0.1977**.

So, the area of the shaded region is **0.1977**.

Would you like more details on how this is calculated or any clarifications?

Here are 5 related questions for further exploration:
1. What is the cumulative probability for \( z = 1.5 \)?
2. How would you find the area between two z-scores, say \( z = -0.85 \) and \( z = 1 \)?
3. What is the total area under the standard normal curve?
4. How does changing the mean or standard deviation affect the z-score calculation?
5. How do you calculate the z-score for a data point given a different mean and standard deviation?

**Tip:** The area under the entire standard normal curve is always 1, since it represents all possible outcomes of a normally distributed random variable.

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1, with z = -0.85.

This problem involves calculating the cumulative probability up to the z-score of -0.85 in a standard normal distribution with mean 0 and standard deviation 1. Learn how to use the z-table or calculator to find that the area of the shaded region is approximately 0.1977.

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