Week 7 — Readings & Resources · Binomial & Normal Models

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objectives covered: Objective 4 — Apply basic probability rules, including conditional probability, and work with random variables. · Objective 5 — Use normal and sampling distributions to reason about variability.

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.

This week's load is deliberately light: ~5 short readings + 3 short videos, grouped by the three ideas from the lecture. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable for the quiz and the midterm next week. Total time is roughly 45–55 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① the binomial setting (the four conditions) → ② computing a binomial probability, and its mean & SD → ③ the normal approximation to the binomial.

A habit to keep: before you trust any worked value below, you already know the in-class anchors — P(exactly 2 of 3 free throws) = 0.375 (= 3/8) and for 100 fair flips, mean 50, SD 5. If a source's number disagrees with the course definitions, trust the course.

① The Binomial Setting (the four conditions: binary · independent · fixed n · same p)

Maps to Lecture Segments 2. Remember the memory hook: B-I-N-S — Binary, Independent, N fixed, Same p. All four must hold.

Reading — "4.3 Binomial Distribution" (OpenStax, Introductory Statistics 2e)
🔗 https://openstax.org/books/introductory-statistics-2e/pages/4-3-binomial-distribution
Why it's assigned: the cleanest authoritative statement of the binomial conditions (and the Bernoulli-trial idea behind them), with the exact formula and worked examples we used in class. Free to read online.
⏱ ~8 min

Reading — "Binomial Distribution: Definition, Formula & Examples" (Scribbr)
🔗 https://www.scribbr.com/statistics/binomial-distribution/
Why it's assigned: a plain-language version of the four conditions and a "is this binomial?" walkthrough — exactly the checklist from Segment 2, including the "without replacement breaks independence" trap.
⏱ ~7 min

Video — "An Introduction to the Binomial Distribution" (jbstatistics)
🔗 https://www.youtube.com/watch?v=qIzC1-9PwQo
Why it earns the click: in 14 minutes it states the conditions, the formula, the mean and variance, and works two probability examples — the whole week's mechanics in one calm pass.
⏱ ~14 min

② Computing a Binomial Probability · Mean (np) & SD (√(np(1−p)))

Maps to Lecture Segments 3 & 5. The formula is ways to arrange k successes × the chance of one such arrangement: P(X = k) = C(n, k) · pᵏ · (1−p)ⁿ⁻ᵏ. Center is np; spread is √(np(1−p)).

Reading — "Binomial probability (basic)" (Khan Academy, article)
🔗 https://www.khanacademy.org/math/ap-statistics/random-variables-ap/binomial-random-variable/a/binomial-probability-basic
Why it's assigned: a tight, example-driven derivation of the binomial probability formula on small, friendly cases — the same "count the arrangements, multiply the chances" logic we used for the free-throw example.
⏱ ~6 min

Reading — "Binomial mean and standard deviation formulas" (Khan Academy, article)
🔗 https://www.khanacademy.org/math/ap-statistics/random-variables-ap/binomial-mean-standard-deviation/a/binomial-mean-and-standard-deviation-formulas
Why it's assigned: shows why μ = np and σ = √(np(1−p)) (the shortcut behind "expect 50 heads, give or take 5") — a good second pass if Segment 5 felt fast.
⏱ ~6 min

Video — "The Binomial Distribution: Crash Course Statistics #15"
🔗 https://www.youtube.com/watch?v=WR0nMTr6uOo
Why it earns the click: the liveliest tour of the binomial — when it applies and how the formula gives the odds of everyday "how many out of n" events.
⏱ ~12 min

③ The Normal Approximation to the Binomial

Maps to Lecture Segment 6. The license to use a bell curve: np ≥ 10 AND n(1−p) ≥ 10 (both must clear it). The normal curve borrows the same center (np) and spread (√(np(1−p))).

Reading — "7.3 Using the Central Limit Theorem" (OpenStax, Introductory Statistics 2e)
🔗 https://openstax.org/books/introductory-statistics-2e/pages/7-3-using-the-central-limit-theorem
Why it's assigned: explains why a large-n binomial smooths into a bell and how to approximate it with a normal curve of mean np and SD √(npq) — the setup we previewed in Segment 6.
Heads-up on the threshold: this text uses np > 5 and nq > 5 (and notes the approximation is "better" when both are ≥ 10). Our course uses the stricter np ≥ 10 and n(1−p) ≥ 10 rule — go with the course rule on the quiz; the texts agree that bigger is safer.
⏱ ~8 min

Video — "The Normal Approximation to the Binomial Distribution" (jbstatistics)
🔗 https://www.youtube.com/watch?v=CCqWkJ_pqNU
Why it earns the click: shows the bars of a binomial turning into a bell and walks through when the approximation is reasonable — the exact picture behind the np ≥ 10 / n(1−p) ≥ 10 check.
⏱ ~10 min

Optional one-stop reference (free online text)

If you'd like one optional reference to skim, OpenIntro Statistics keeps its full text and per-section videos free to read online. Chapter 4 ("Distributions") covers everything in this week — 4.3A Binomial distribution and 4.3B Normal approximation to the binomial — with short videos for each.
🔗 https://www.openintro.org/book/os/
Why it's here: a reputable, currently-available reference you can return to in Week 9 (the normal distribution) and beyond — entirely optional this week.

Pick-one quick path (≈15 min total)

In a hurry? Do exactly these three and you'll be ready for the quiz:
1. Read OpenStax 4.3 — Binomial Distribution (group ①) for the conditions + formula.
2. Read Khan — Binomial mean and SD formulas (group ②).
3. Watch jbstatistics — The Normal Approximation to the Binomial (group ③).

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell Prof. Rivera and use the OpenIntro reference above in the meantime.