Lecture Notes: Introduction to the Normal Distribution

Lecture Information

• Title: Stack Quest on Normal Distribution
• Presented by: University of North Carolina at Chapel Hill, Genetics Department

Key Topics Covered

Introduction to Normal Distribution

• Often called Gaussian distribution or bell-shaped curve.
• Symmetrical curve resembling a bell.
• Commonly used to represent data such as human height measurements.
  • Short, average, or tall heights.
  • Y-axis: Relative probability of observing a certain height.
  • Rare heights (very short or tall) reflected by low areas of the curve.
  • Average heights reflected by tall areas of the curve.

Example: Human Height Distributions

• Baby Height Distribution:

  • Average height: 20 inches.
  • Curve is tall, indicating less variance (fewer height options).
  • Small standard deviation: 0.6

• Adult Height Distribution:

  • Average height: 70 inches.
  • Curve is wider and shorter, indicating more variance (more height options).
  • Larger standard deviation: 4

Understanding Standard Deviation

• Defines the width of the curve.
• Helps determine how likely it is to measure a specific range around the mean.
• 95% Rule:
  • 95% of measurements fall within ±2 standard deviations around the mean.
  • Babies: Measurements fall between 20 ± 1.2 inches.
  • Adults: Measurements fall between 70 ± 8 inches.

Drawing a Normal Distribution

1. Average Measurement: Determines the center of the curve.
2. Standard Deviation: Determines the width and height of the curve.
   • Wider curve: Shorter height.
   • Narrower curve: Taller height.

Applications of Normal Distribution

• Common in nature and statistics.
• Examples: Weight, commuting times, etc.

The Central Limit Theorem (CLT)

• Anticipated future topic.
• CLT explains why normal distribution appears frequently in nature and statistics.

Conclusion

• Encouragement to subscribe and suggest future topics.
• Sign-off: "Quest on"