https://file.aiquickdraw.com/mathbot/file/1726262635020m8snotmn.jpg

The problem asks to find the probability of the shaded region in a uniform distribution.

The graph shows a uniform distribution where the total probability must sum to 1. The height of the rectangle is \(\frac{1}{9}\), which suggests the range of the uniform distribution has a total length of 9 units.

### Step-by-Step Solution:
1. **Total Range of Distribution**: The uniform distribution seems to range from \(x = 0\) to \(x = 9\). The total length of this range is 9 units.
  
2. **Shaded Region Range**: The shaded region spans from \(x = 6\) to \(x = 8\), so the length of the shaded region is:
   \[
   \text{Shaded length} = 8 - 6 = 2
   \]

3. **Height of the Distribution**: The height is \(\frac{1}{9}\), as labeled on the y-axis.

4. **Probability of Shaded Region**: The probability for a continuous uniform distribution is the area under the curve over the shaded region. The area is calculated by multiplying the width (length of the shaded region) by the height:
   \[
   \text{Probability} = \text{height} \times \text{width} = \frac{1}{9} \times 2 = \frac{2}{9}
   \]

Thus, the probability of the shaded region is \(\frac{2}{9}\).

Would you like more details or have any other questions?

### Related Questions:
1. What is the formula for finding the probability in a continuous uniform distribution?
2. How does the total area under a uniform distribution curve relate to probability?
3. Can the height of the uniform distribution change based on different ranges?
4. How would the probability change if the shaded region spanned from \(x = 5\) to \(x = 8\)?
5. What happens to the probability if the total range of the distribution increases?

**Tip**: Always ensure the area under the entire uniform distribution sums to 1 when calculating probabilities!

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

Calculate the probability of a shaded region in a uniform distribution. This problem involves determining the height and width of the shaded area under the curve and applying the formula for continuous probability distribution. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation