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The question asks to find the bone density test scores that separate the lowest 15% and highest 15% of a normally distributed population, with a mean of 0 and a standard deviation of 1. It also asks for a sketch of the region corresponding to these values.

### Solution Process:
Given that the test scores are normally distributed, we use the **Z-scores** to find the cutoff values.

1. **Identify the percentile levels:**
   - The lowest 15% corresponds to the left tail of the distribution.
   - The highest 15% corresponds to the right tail of the distribution.
   - Therefore, we are looking for the Z-scores at the 15th percentile and the 85th percentile (because 100% - 15% = 85%).

2. **Use the Z-table:**
   - From standard normal distribution tables or a calculator, the Z-score corresponding to the 15th percentile is approximately **-1.04**.
   - Similarly, the Z-score corresponding to the 85th percentile is approximately **+1.04**.

### Bone Density Scores:
Since the mean is 0 and the standard deviation is 1, the bone density scores that mark the 15% cutoffs are simply the Z-scores:
- **Lower score (15th percentile):** -1.04
- **Upper score (85th percentile):** +1.04

### The Correct Graph:
The correct graph should highlight the regions below the Z-score of -1.04 and above the Z-score of +1.04, which is indicated by **option C** (as you have correctly selected).

### Final Answer:
The bone density test scores are **-1.04, 1.04** (rounded to two decimal places).

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Would you like further details on Z-scores or how to interpret this graph?

Here are some related questions:
1. What is a Z-score and how is it calculated?
2. How do you find Z-scores for specific percentiles without a table?
3. What is the empirical rule in normal distributions and how does it apply here?
4. How would the solution change if the standard deviation were different from 1?
5. How do we calculate probabilities between two Z-scores?

**Tip:** Always double-check your Z-tables or use statistical software to ensure precision when finding percentile-based Z-scores!

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the bone density test scores that can be used as cutoff values separating the lowest 15% and highest 15%, indicating levels that are too low or too high, respectively. Sketch the region containing the lowest 15% and highest 15%.

Learn how to find Z-scores that separate the lowest 15% and highest 15% of bone density test scores in a normally distributed population. This problem involves using normal distribution tables, Z-scores, and percentiles, suitable for students in college-level statistics or advanced high school courses.

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