x	P(x)
0	0.001
1	0.018
2	0.039
3	0.114
4	0.206
5	0.235
6	0.208
7	0.116
8	0.037
9	0.012
10	0.014Use the range rule of thumb to identify a range of values that are not significant.
The maximum value in this range is 
  
9 girls.
​(Round to one decimal place as​ needed.)

To use the **range rule of thumb** to identify a range of values that are not significant, we typically follow these steps:

1. **Calculate the mean** (\(\mu\)) of the distribution.
2. **Calculate the standard deviation** (\(\sigma\)) of the distribution.
3. Use the range rule of thumb formula to identify the range:
   - The lower bound is \(\mu - 2\sigma\).
   - The upper bound is \(\mu + 2\sigma\).

### Step 1: Calculate the mean (\(\mu\))

The mean for a discrete probability distribution is given by:

\[
\mu = \sum [x \cdot P(x)]
\]

Let’s calculate it.

### Step 2: Calculate the standard deviation (\(\sigma\))

The standard deviation for a discrete probability distribution is given by:

\[
\sigma = \sqrt{\sum [(x - \mu)^2 \cdot P(x)]}
\]

After we find both \(\mu\) and \(\sigma\), we will use the range rule of thumb to identify the range of values.

Let me calculate that for you.The mean (\(\mu\)) of the distribution is approximately \(5.04\), and the standard deviation (\(\sigma\)) is approximately \(1.69\).

Using the range rule of thumb:
- **Lower bound** = \( \mu - 2\sigma \approx 1.65\)
- **Upper bound** = \( \mu + 2\sigma \approx 8.43\)

Thus, the range of values that are considered not significant is from approximately **1.65 to 8.43**. Since the question asks for the maximum value and specifies rounding to one decimal place, the **maximum value in this range is 8.4** girls.

Do you have any questions or need further details?

Here are 5 related questions:
1. How does the range rule of thumb work in practice for real-life data sets?
2. How can I use this approach to determine outliers in a probability distribution?
3. What are other methods to determine significant values in a distribution?
4. How would the result change if the probabilities were slightly different?
5. How does the standard deviation affect the spread of a probability distribution?

**Tip:** The range rule of thumb provides a quick estimate, but more rigorous methods (like z-scores) can offer a more precise understanding of significance.

Use the range rule of thumb to identify a range of values that are not significant. The maximum value in this range is 9 girls. (Round to one decimal place as needed.)

Learn how to apply the range rule of thumb to identify significant values in a probability distribution with a step-by-step example. This problem involves calculating the mean and standard deviation for a given probability distribution and determining the range of non-significant values. Suitable for 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