Lesson 9
Normal distribution
Big question
Why does the bell curve show up so often?
Lesson progress
Complete checkpoints as you learn
Learning objectives
- Explain normal distribution in plain language.
- Use normal distribution correctly in an interpretation.
- Connect the lesson idea to a formula, graph, Python result, or real example.
Simple explanation
The normal distribution is a smooth, symmetric distribution. It is useful because many averages and estimation errors behave approximately normally in large samples.
Key terms
- Normal distribution
- A bell-shaped distribution described by a mean and standard deviation.
- Mean
- The center of the distribution.
- Standard deviation
- The typical distance from the mean.
- Symmetry
- The left and right sides have matching shape around the center.
Normal notation
Read this as: X is normally distributed with mean mu and variance sigma squared.
Example
If test scores are roughly bell-shaped, most students are near the average and fewer students are far above or below it.
Draw a normal curve
1import numpy as np2import matplotlib.pyplot as plt3 4x = np.linspace(-3, 3, 100)5y = (1 / np.sqrt(2 * np.pi)) * np.exp(-0.5 * x**2)6plt.plot(x, y)7plt.title("Standard normal curve")8plt.show()Checkpoint activity
Pause and explain this lesson's main idea in your own words before moving forward.
Try it yourself
Write one plain-English sentence explaining the main idea from this lesson.
Common mistakes
Check these before you move on.
A regression coefficient describes a pattern unless the assumptions or research design support a causal interpretation.
Quick quiz
What gives the normal distribution its spread?
Key takeaway
The normal distribution is a helpful benchmark for thinking about averages and uncertainty.