Normal Distribution 🔔

The Normal Distribution is the most important continuous probability distribution in statistics. It is often called the Gaussian Distribution or the Bell Curve.

Why is it important? 🌟

Most naturally occurring phenomena follow this pattern:

• Heights of people.
• IQ Scores.
• Marks in an exam.
• Errors in measurement.

The Bell Curve 📉

The graph of a Normal Distribution is a bell-shaped curve that extends indefinitely in both directions.

Properties of Normal Curve 📋

1. Symmetrical: It is perfectly symmetrical about the Mean (μ). 50% area is on left, 50% on right.
2. Unimodal: It has only one peak (Mode).
3. Equality: Mean = Median = Mode.
4. Asymptotic: The curve gets closer and closer to the X-axis but theoretically never touches it.
5. Area Properties:
   • Mean ± 1 SD (σ): Covers 68.26% of data.
   • Mean ± 2 SD (σ): Covers 95.45% of data.
   • Mean ± 3 SD (σ): Covers 99.73% of data.

Standard Normal Variate (Z) 📏

To calculate probabilities for any Normal Distribution, we convert variables (X) into a Standard Score (Z).

Z = (X - μ) / σ

• μ: Mean of the distribution.
• σ: Standard Deviation.
• The Standard Normal Distribution has Mean = 0 and SD = 1.

Comparison 🆚