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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. round the answer to four decimal places as needed.

The graph shows a standard normal distribution, where the mean is 0 and the standard deviation is 1. The shaded region is bounded by two z-scores: \( z = -0.86 \) and \( z = 1.26 \). 

To find the area of the shaded region, we calculate the cumulative area under the standard normal curve between these two z-scores. This is done by using the cumulative distribution function (CDF) for the standard normal distribution.

Steps:
1. Find the cumulative probability corresponding to \( z = 1.26 \).
2. Find the cumulative probability corresponding to \( z = -0.86 \).
3. Subtract the cumulative probability of \( z = -0.86 \) from that of \( z = 1.26 \) to get the area of the shaded region.

Let's calculate this now.The area of the shaded region between the z-scores \( z = -0.86 \) and \( z = 1.26 \) is approximately 0.7013 (rounded to four decimal places).

Would you like further details on this calculation or have any other questions?

Here are some related questions for further exploration:
1. How is the cumulative distribution function (CDF) used in normal distribution calculations?
2. What is the significance of z-scores in statistics?
3. How do you calculate probabilities for standard normal distributions without a table?
4. What are the properties of a standard normal distribution?
5. How can confidence intervals be visualized using normal distribution graphs?

**Tip:** You can use standard normal tables or statistical software to quickly find areas under the normal curve based on z-scores.

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. Round the answer to four decimal places as needed.

Learn how to calculate the area of the shaded region between z-scores -0.86 and 1.26 in a standard normal distribution. This problem uses the cumulative distribution function (CDF) and z-scores to find the probability. Suitable for students in Grades 11-12.

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