https://file.aiquickdraw.com/mathbot/file/172828134799188j7igbc.jpg

To solve this problem, we need to find the probability of the shaded region under the uniform distribution.

### Key information:
- The height of the distribution is \( \frac{1}{9} \).
- The distribution is uniform, so the probability is proportional to the area of the shaded region.

### Step-by-step solution:

1. **Identify the length of the shaded region:**
   - From the graph, the shaded region lies between \( x = 6 \) and \( x = 8 \). 
   - The length of the shaded region is \( 8 - 6 = 2 \).

2. **Find the area of the shaded region:**
   - The area of a region under the curve in a uniform distribution is given by:
     \[
     \text{Area} = \text{length of region} \times \text{height of distribution}
     \]
   - Substituting the values:
     \[
     \text{Area} = 2 \times \frac{1}{9} = \frac{2}{9}
     \]

3. **Conclusion:**
   - The probability of the shaded region is \( \frac{2}{9} \).

This is the final answer: \( \frac{2}{9} \).

Would you like further details, or have any questions? Here are five related questions that might interest you:

1. What is a uniform distribution and how is it defined mathematically?
2. How would the probability change if the shaded region extended from \( x = 4 \) to \( x = 9 \)?
3. Can the probability ever exceed 1 in a probability distribution?
4. How is the total area under a probability density function related to probability?
5. What are the properties of continuous versus discrete uniform distributions?

**Tip:** The area under a probability density function (PDF) over a given interval represents the probability for that interval, and the total area under the PDF for the entire distribution equals 1.

Given the uniform distribution below, find the probability of the shaded region. Give your answer in fraction form.

Learn how to find the probability of a shaded region in a uniform distribution with this step-by-step solution. The problem involves calculating the area of a region under a probability density function (PDF) and is suitable for students in Grades 9-11.

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