Lesson 4: 2.4 The Empirical Rule and Assessing Normality

What makes a "Normal" distribution different from just any symmetric, bell-shaped distribution?

If we know the mean and standard deviation of a Normal distribution, why does that allow us to predict the "spread" of the entire population?

Normal Distribution

Normal Curve

68–95–99.7 Rule (Empirical Rule)

HSS-ID.A.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.

This is high-yield for the SAT. Students are often given a mean and standard deviation and asked to identify the range that contains 95% of the data. Knowing the Empirical Rule allows them to solve these without a calculator.

To introduce the most important probability model in statistics. It teaches students that the standard deviation is the "natural ruler" for a Normal distribution.

The Problem: The distribution of Iowa Test of Basic Skills (ITBS) vocabulary scores for seventh-grade students in Gary, Indiana, is close to Normal with mean of 6.84$and standard deviation of 1.55.

Part A: Sketch the Normal curve for this distribution.

Part B: Between what two scores do the middle 68% of students lie?

Inflection Points: Students often struggle to place the standard deviation marks on the graph. Remind them that sigma is located at the inflection point—where the curve changes from "cupped down" to "cupped up."

Support: Provide "Pre-drawn" Normal curves where students only have to fill in the numerical labels on the axis.

Extension: Ask students to calculate what percentage of data falls outside of 2 standard deviations (the "tails").

Teacher assigns examples from the textbook and other resources.

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