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The question involves a **normally distributed bone density test score** with a mean \( \mu = 0 \) and a standard deviation \( \sigma = 1 \). The task is to determine which graph represents the 9th percentile (denoted as \( P_9 \)) and calculate the corresponding score.

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### **Solution:**

1. **Understanding Percentile \( P_9 \):**
   - The **9th percentile** means that 9% of the distribution lies below that point, and 91% lies above it.
   - We need to determine the **z-score** that corresponds to the **cumulative probability of 0.09** in a standard normal distribution.

2. **Finding the z-score for the 9th percentile:**
   - Using standard z-tables or a calculator:
     \[ P(Z \leq z) = 0.09 \implies z \approx -1.34 \]
   - This means that a z-score of approximately **-1.34** separates the bottom 9% from the rest of the distribution.

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### **Identifying the Correct

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 P9, the 9th percentile. Which graph represents P9? Choose the correct graph below. The bone density score corresponding to P9 is (rounded to two decimal places).

In this problem, we explore how to calculate the 9th percentile of a normally distributed bone density test score with a mean of 0 and standard deviation of 1. Find out how to use z-scores and cumulative probabilities to represent the percentile on a graph.

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