Week 7 — Readings & Resources · The Binomial Distribution
Course: Introduction to Statistics (18-week generic edition)
Objective covered: Objective 4 — the binomial model: recognize the setting, compute exact probabilities, and give the mean and SD of a count of successes.
Your primary reading is Chapter 7 (in this module). Everything below is the optional, go-deeper layer.
How to use this page
Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded, and nothing costs money.
The load is deliberately light: 4 short readings + 4 short videos, grouped by the four big ideas of the week. Read or watch one item per group and you're well prepared; do all of them and you'll be very comfortable. Total time is roughly 60–70 minutes if you do everything, far less if you pick one per group.
Order that matches the chapter and lecture: ① the binomial setting (B·I·N·S) → ② the formula for exactly-k → ③ mean np and SD √(np(1−p)) → ④ shape, technology, and the bridge to the normal.
A habit to keep this week: every time a resource states a binomial answer, check it against the week's toolkit — does the setting pass B·I·N·S? did they count the ways? is the question "exactly" or "at least"?
① The Binomial Setting — is it binomial at all?
Maps to Chapter 7, Section 1 and Lecture Segment 2. The gatekeeper: B·I·N·S — Binary, Independent, Number fixed, Same p. No B·I·N·S, no binomial.
Reading — 4.3: The Binomial Distribution (LibreTexts Statistics, Shafer & Zhang)
🔗 https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/04%3A_Discrete_Random_Variables/4.03%3A_The_Binomial_Distribution
Why it's assigned: the cleanest statement of the criteria a binomial experiment must meet — identical in substance to our B·I·N·S checklist — with worked examples that also preview the formula and the mean/SD shortcuts.
⏱ ~10 min
Video — The Binomial Distribution: Crash Course Statistics #15 (video, ~12 min, captioned)
🔗 https://www.youtube.com/watch?v=WR0nMTr6uOo
Why it earns the click: the liveliest tour of the whole week in one sitting — what makes a setting binomial, why the formula looks the way it does, and where the model shows up in real life.
② The Formula — ways × wins × losses
Maps to Chapter 7, Section 2 and Lecture Segments 3–4. The piece everyone forgets is the ways factor C(n, k) — skip it and your answer is too small by exactly that factor.
Reading — Binomial Probability Distribution (Stat Trek)
🔗 https://stattrek.com/probability-distributions/binomial
Why it's assigned: walks the formula slowly with several fully worked examples, and includes a free binomial calculator you can use to check your own hand computations — a third weapon alongside the formula and =BINOM.DIST.
⏱ ~8 min
Video — An Introduction to the Binomial Distribution (jbstatistics) (video, ~15 min, captioned)
🔗 https://www.youtube.com/watch?v=qIzC1-9PwQo
Why it earns the click: the most careful on-screen build of the formula — one specific sequence first, then counting the arrangements — exactly the three-move construction from the lecture.
③ Mean & SD — what to expect, give or take
Maps to Chapter 7, Section 3 and Lecture Segment 5. μ = np and σ = √(np(1−p)) — expected, not guaranteed, with the SD as the built-in give-or-take.
Reading — Binomial Distribution (Online Statistics Education, Rice University)
🔗 https://onlinestatbook.com/2/probability/binomial.html
Why it's assigned: a compact chapter section that derives the probabilities for a small example, then states the mean and variance formulas plainly — good for seeing the Week 6 long way and this week's shortcut side by side.
⏱ ~8 min
Video — The Binomial Distribution and Test, Clearly Explained!!! (StatQuest with Josh Starmer) (video, ~10 min, captioned)
🔗 https://www.youtube.com/watch?v=J8jNoF-K8E8
Why it earns the click: StatQuest's trademark small-steps style, using the formula on a real yes/no question and showing what the answer means — plus a gentle first taste of how binomial probabilities get used for inference much later in the course.
④ Shape & the Bridge — where the binomial sits, and where it's heading
Maps to Chapter 7, Sections 4–5 and Lecture Segments 6–7. Symmetric at p = 0.5, skewed at extreme p — and as n grows, the histogram reaches for a bell. Next week the bell gets its name.
Reading — Probability Distribution | Formula, Types, & Examples (Scribbr)
🔗 https://www.scribbr.com/statistics/probability-distributions/
Why it's assigned: zooms out to the family tree of probability distributions, showing where the binomial sits among the other named machines — a review of Week 6's ideas and a preview of the normal curve waiting in Week 8.
⏱ ~9 min
Video — Binomial distributions | Probabilities of probabilities, part 1 (3Blue1Brown) (video, ~13 min, captioned)
🔗 https://www.youtube.com/watch?v=8idr1WZ1A7Q
Why it earns the click: the most beautiful animation of binomial histograms you will ever see — watch the bars rise, shift, and change shape as n and p move. (The closing minutes tease ideas beyond our course; enjoy the pictures and don't worry about the ending.)
Optional one-stop reference (free online text)
If you'd like one optional reference to skim, OpenStax Introductory Statistics 2e keeps its full text free to read online. Section 4.3 (Binomial Distribution) covers this week end to end — the characteristics of a binomial experiment, the notation X ~ B(n, p), and the mean and standard deviation formulas.
🔗 https://openstax.org/books/introductory-statistics-2e/pages/4-3-binomial-distribution
Why it's here: a reputable, currently-available reference you can return to in later weeks — entirely optional this week.
Pick-one quick path (≈25 min total)
In a hurry? You've read Chapter 7 — then do exactly these two and you'll be ready for the quiz:
1. Watch Crash Course Statistics #15 — The Binomial Distribution (group ①).
2. Watch An Introduction to the Binomial Distribution — jbstatistics (group ②).
Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the OpenStax reference above in the meantime.