Week 7 — Binomial & Normal Models

Welcome to your Week 7 Start Here page.

Why this matters

Counting successes in repeated tries is everyday work: a clinic manager plans for missed appointments, and a quality inspector counts faulty parts. Both reach for the binomial model this week, and for the normal curve when counts get large.

In plain language

Many questions in life come down to counting how many times something happens in a set number of tries, such as how many of 10 guessed quiz answers are right. This week you learn the binomial model (a ready-made probability model for counting successes in repeated, independent tries), so you can find those chances without listing every outcome. You will also find the average count and its typical spread. Then you meet the normal curve (a smooth, bell-shaped model), see when it can stand in for a count, and see why it is the working model for many measurements.

• Already covered: Weeks 1 to 4 described data; Weeks 5 and 6 measured chance and random variables.
• This week: the binomial model, its mean and spread, its shape, and a first look at the normal curve.
• How they connect: Week 5's rules build each binomial chance; Week 6's mean becomes np.
• Where we're going next: Week 8 reviews for the midterm and adds z-scores.

Focus

If you count successes in a fixed number of tries, how likely is each count, and when can a smooth curve stand in?

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

• [ ] check the four binomial conditions
• [ ] find a binomial chance by formula and by spreadsheet
• [ ] find and explain the binomial mean and standard deviation
• [ ] decide when a normal curve may stand in for a count

To-do

Plan your week

1. Read Chapter 7 (about 45 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 chance a pure guesser scores 5 or more on the 10-question quiz, and say why a normal curve cannot stand in for that count.

You've got this

Take it in order, and ask your instructor early if a step snags.

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