The Empirical Rule Visualizer is an interactive tool designed to help users understand and apply the Empirical Rule (also known as the 68-95-99.7 Rule) in statistics. This rule is a cornerstone of normal distribution analysis, providing insights into how data is distributed around the mean.

Key Features:

1. Interactive Bell Curve : A dynamic visualization of the normal distribution curve with highlighted areas for 68%, 95%, and 99.7% of the data.
2. Customizable Inputs : Users can input their own mean and standard deviation values to generate personalized visualizations.
3. PDF Download : Export the generated visualization and statistical breakdown as a PDF for sharing or reporting purposes.
4. Colorful and Modern Design : Eye-catching design with vibrant colors to make the tool visually appealing and easy to interpret.
5. Self-Contained : The tool operates within its own container, ensuring it doesn’t interfere with the page header or footer.

Use Cases:

• Educational Purposes : Teachers and students can use this tool to learn and teach the Empirical Rule effectively.
• Data Analysis : Analysts can quickly visualize the spread of their data under the assumption of normality.
• Reporting : Professionals can export visualizations to include in reports or presentations.

How It Works:

1. Introduction : The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
2. Input Fields : Users enter the mean and standard deviation of their dataset.
3. Visualization : The tool dynamically updates the bell curve to reflect the entered values, highlighting the respective percentages.
4. Export : Users can download the visualization and data summary as a PDF for further use.