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The question asks you to identify the graph that correctly represents \( P_{18} \), the 18th percentile of a normally distributed set of bone density test scores with a mean of 0 and a standard deviation of 1. 

The 18th percentile refers to the value below which 18% of the data falls in a normal distribution. Since the distribution is normal (mean = 0, standard deviation = 1), we are looking for the point on the x-axis that corresponds to 18% of the area under the curve to the left.

Looking at the four choices, graph **C** is selected as correct. In this graph:
- The shaded region on the left represents the lower 18% of the distribution, which correctly visualizes \( P_{18} \), the 18th percentile.

### To find the exact bone density score corresponding to \( P_{18} \):
- The z-score for the 18th percentile can be found using a standard normal table or calculator.
- From the table, the z-score corresponding to the 18th percentile is approximately \( z = -0.92 \).
  
Thus, the bone density score \( P_{18} \) is approximately -0.92.

Would you like further clarification or more details on how the z-score is calculated?

### Related Questions:
1. What does the 50th percentile represent in a normal distribution?
2. How would the graph change if the standard deviation were greater than 1?
3. Can you explain how to find percentiles using a z-score table?
4. What is the z-score for the 5th percentile in a normal distribution?
5. How does the shape of the graph change for a left-skewed distribution?

### Tip:
When working with percentiles, always remember that the z-score gives you the number of standard deviations from the mean, helping you determine the specific value for that percentile.

Assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find P18, the 18th percentile. This is the bone density score separating the bottom 18% from the top 82%. Which graph represents P18? Choose the correct graph below.

Find the 18th percentile (P18) of a bone density test score using normal distribution with a mean of 0 and standard deviation of 1. This problem focuses on z-scores and graph identification to determine the value of P18. Suitable for undergraduate students.

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