Title: Week 7 Overview — Start Here
Course: Introduction to Statistics (18-Week Generic Edition)

Welcome to Week 7: The Binomial Distribution

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

Three questions that sound unrelated: how likely is it that exactly 2 of 5 emailed customers click? How often does a 50-50 free-throw shooter make all 4 of her shots? How many true/false questions does pure guessing get right? Surprise: they're all the same question — a fixed number of yes/no tries, count the wins. That pattern is so common it has its own famous machine, the binomial distribution — the first random variable you'll meet that comes pre-solved: a recognition checklist, a formula, a mean-and-SD shortcut, and its own spreadsheet function.

The week's big question

"When you try something n times and count the wins, what exactly are the chances — and what should you expect, give or take?"

Last week you built probability distributions by hand, row by row, and summarized them with E(X). This week, one hugely common random variable generates its entire distribution from just two numbers, n and p — and by the end of the week you'll wield it three ways: by formula, by table, and by machine.

By the end of this week, you can…

Use this as a checklist. If you can do all five out loud, you're ready for the quiz.

- [ ] Spot a binomial setting with the B·I·N·S checklist — Binary outcome, Independent trials, Number of trials fixed, Same p — and refuse the impostors (no fixed n; without-replacement draws).
- [ ] Name n and p in a described situation, including when "success" is something bad (a no-show, a miss).
- [ ] Compute P(exactly k) with the formula — ways × wins × losses — never forgetting the ways factor C(n, k).
- [ ] Shortcut "at least one" with the complement: 1 − P(none).
- [ ] Give the mean np and SD √(np(1−p)) and say them in words — "expect about , give or take about " — then use them to judge whether a result is ordinary wobble or a real surprise.

What to do this week, in order

The table below lists the week's items in working order, with what each is worth and when it's due.

# | Do this | Type | Due
1 | Read Chapter 7 — the module's primary reading | Chapter (ungraded prep) | Early in the week
2 | Skim the slides (Deck 7) and the Week 7 lecture outline; browse the Readings & Resources links that interest you | Prep (ungraded) | Alongside class
3 | Lecture Tutorial 7 — work the binomial with your chatbot (mini-table included), then submit the share link + Completion Summary | Tutorial · graded (Lecture tutorials, 20% group) | End of Week 7
4 | Practice exercises — quick reps with the AI coach | Practice · ungraded | Before the quiz (recommended)
5 | Data Lab 7 — "Two Hundred Rounds of Four" — simulate a 50-50 shooter 200 times and test the binomial model against your own data | Data lab · graded (Data labs, 15% group) | End of Week 7
6 | Quiz 7 — B·I·N·S, the formula, at-least-one, mean/SD, =BINOM.DIST, shape | Quiz · graded (Quizzes, 15% group) · closed to AI | End of Week 7
7 | Discussion 7 — "The Hot-Hand Question" — interrogate a real streak with your chatbot, post the AI summary + chat link, then reply to two classmates | Discussion · graded (Discussions, 15% group) | Initial post two days before week's end; replies by end of Week 7
8 | Assignment 7 — "Expected, Not Guaranteed" — four AI-coached problems; submit the report (score on line 1) + chat link | Assignment · graded (Assignments, 25% group) | End of Week 7

Heads-up on the AI work: chatbots are famously sloppy with this exact topic — they drop the ways factor C(n, k), or quietly hand you a cumulative probability when you asked for "exactly k." This week you hold three weapons that must always agree — the formula, the mini-table, and =BINOM.DIST — so catching the model is easier than ever. Catching it is the point.

Late policy reminder: 10% off per day late. If life happens, reach out to your instructor before the deadline — early is always easier.

How to succeed this week

- Checklist before formula. The most-lost points aren't arithmetic — they're using the binomial where it doesn't apply. Run B·I·N·S out loud first; if there's no fixed n or the draws are without replacement, stop.
- Count the ways. Say the formula as "ways × wins × losses." If your probability feels suspiciously tiny, you probably skipped the ×C(n, k).
- Read like a lawyer. Exactly 2 is one bar; at least 2 is a tail; at least one is the express lane — 1 − P(none).
- Two numbers beat six. μ = np and σ = √(np(1−p)) answer "what should I expect?" faster than any table — and expected, not guaranteed is the phrase that keeps them honest.
- Make the machine agree with you. Every answer you compute this week can be checked with =BINOM.DIST(k, n, p, FALSE) in ten seconds. If hand and machine disagree, one of you misread the question — find out which.

You already own every ingredient — Week 5's independence and complements, Week 6's expected value. This week just bolts them together into your first named machine. Come to the first session ready to argue about hot streaks.