Week 9 — The Normal Distribution

Welcome to your Week 9 Start Here page.

Why this matters

How far is a value from the middle, and how common is that? A nurse judging whether one patient's reading is unusual and a transit planner deciding how much slack a bus timetable needs both answer it with the normal model.

In plain language

Many measurements pile up in the middle and thin out evenly on both sides, like a bell. This week you learn the normal distribution (the bell-shaped model set by a center and a spread) and how to use it to answer "how common is that?" You will learn a quick rule of thumb for the bell, and a way to put any value on one common scale. You will find the share of values below a cutoff, and the cutoff that matches a share. Then you will learn to check whether a bell is a fair description of real data before you lean on it.

• Already covered: Weeks 1 to 8 described data, built probability and the binomial, and added the z-score.
• This week: the normal model, the empirical rule, standardizing, forward and inverse calculations, and model checks.
• How they connect: last week's z-score now reads off a bell as a share of values.
• Where we're going next: Week 10 shows why averages follow this same bell.

Focus

What does a bell-shaped model buy you, and when is it fair to use one?

By the end of this module, you should be able to:

• [ ] use the empirical rule and say when it does not apply
• [ ] standardize a value with a z-score
• [ ] find a share below or above a value, and the value for a share
• [ ] judge whether a normal model is reasonable for real data

To-do

Plan your week

1. Read Chapter 9 (about 40 minutes), then the lecture and slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Data Lab (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

This week's checkpoint: find the 95th percentile commute under the model with mean 32 minutes and standard deviation 6 minutes, and say what it means.

You've got this

Sketch the bell before every calculation, and ask your instructor early if a step snags.

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