A data distribution is bell-shaped, with a mean of 50 and a standard deviation of 15. Use the Empirical Rule to approximate the percentage of data between 20 and 80.

The Empirical Rule, also known as the 68-95-99.7 rule, is used to approximate the percentage of data that falls within 1, 2, or 3 standard deviations from the mean in a normal distribution.

Given:
- Mean (μ) = 50
- Standard deviation (σ) = 15

We need to find the approximate percentage of data between 20 and 80.

### Step-by-Step Solution:

1. **Convert the values to z-scores (in terms of standard deviations):**
   - \(20\) is:
     \[
     z_1 = \frac{20 - 50}{15} = \frac{-30}{15} = -2
     \]
   - \(80\) is:
     \[
     z_2 = \frac{80 - 50}{15} = \frac{30}{15} = 2
     \]

2. **Apply the Empirical Rule:**
   - According to the Empirical Rule:
     - About 68% of the data lies within 1 standard deviation of the mean.
     - About 95% of the data lies within 2 standard deviations of the mean.
     - About 99.7% of the data lies within 3 standard deviations of the mean.

3. **Interpret the result:**
   - Since both 20 and 80 are 2 standard deviations from the mean, about **95%** of the data lies between these values.

### Final Answer:
Approximately **95%** of the data falls between 20 and 80.

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Would you like more details on this process or have any questions?

Here are five related questions to explore:
1. What percentage of data falls within 1 standard deviation from the mean?
2. How do you calculate a z-score for a given value?
3. What does it mean for data to be "normally distributed"?
4. What percentage of data is outside of 3 standard deviations from the mean?
5. How does the Empirical Rule compare to Chebyshev’s Theorem?

**Tip:** The Empirical Rule applies specifically to normal (bell-shaped) distributions. For non-normal distributions, other methods like Chebyshev’s Theorem are more appropriate.

A data distribution is bell-shaped, with a mean of 50 and a standard deviation of 15. Use the Empirical Rule to approximate the percentage of data between 20 and 80.

Learn how to use the Empirical Rule to approximate the percentage of data between 20 and 80 in a bell-shaped distribution. With a mean of 50 and standard deviation of 15, find out how 95% of the data falls within this range. Perfect for high school students in Grades 10-12.

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