AP Statistics Lesson

The Empirical Rule: Unlocking the Normal Distribution

Shared by A STEM Educator

11th GradeBTC Style / Thinking Classrooms50 min

Learning Objective

Students will apply the 68-95-99.7 Empirical Rule to calculate probabilities and percentages for normally distributed data by identifying regions under the normal curve relative to the mean and standard deviation.

Lesson Overview

Students progress from reading a normal curve and locating standard deviations to applying the 68-95-99.7 rule in increasingly complex real-world contexts, culminating in reverse problems and multi-region calculations.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors if possible)
Pencils and paper for notes

Scaffolded Task Progression

1Task 1

A normal distribution has mean

μ = 100

and standard deviation

σ = 15

(like an IQ score scale).

Draw and label a normal curve on your whiteboard. Mark the mean in the center. Then mark and label the values that are

1 σ

2 σ

, and

3 σ

above AND below the mean.

What six values should appear on your number line?

2Task 2

Using the same IQ distribution (

μ = 100

σ = 15

), your teacher tells you:
- 68% of data falls within

1 σ

of the mean
- 95% of data falls within

2 σ

of the mean
- 99.7% of data falls within

3 σ

of the mean

Shade and label these three regions on your curve. Then answer:

What percentage of people have an IQ between 85 and 115?

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