Week 9 — Readings & Resources · The Normal Distribution

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective covered: Objective 5 — Use normal 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: ~4 short readings + ~4 short videos, grouped by the four 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. 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 density curves & the normal shape → ② the 68–95–99.7 (empirical) rule → ③ z-scores (standardizing) → ④ z-score → area / percentile, and assessing normality.

A habit to start now: the one number you'll lean on all week is the z-score — how many standard deviations from the mean is this value? As you read, keep asking it: a value's z-score is the whole story of how unusual it is.

One thing the readings can't replace: in this course we supply the z-table values (z = 0, ±0.5, ±1, ±1.5, ±2, ±2.5, ±3) inside the tutorial, practice, quiz, and assignment, and every problem is built to land exactly on them. So when a reading or video looks up a value in a big z-table, just follow the idea — you'll never have to recall a table value here.

① Density Curves & the Normal (Bell) Shape

Maps to Lecture Segment 2. The one rule that runs the week: the total area under a density curve is 1, so any area under it is a proportion — the share of data in that region.

Reading — "Normal Distribution | Examples, Formulas & Uses" (Scribbr)
🔗 https://www.scribbr.com/statistics/normal-distribution/
Why it's assigned: the cleanest plain-language picture of the bell curve — symmetric, single-peaked, pinned down by its mean μ and standard deviation σ — exactly the model we built in class.
⏱ ~8 min

Reading — "Normal distributions review" (Khan Academy, article)
🔗 https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data/normal-distributions-library/a/normal-distributions-review
Why it's assigned: a tight, example-driven recap of reading areas under a normal curve as proportions — a good second pass if the first reading felt fast.
⏱ ~5 min

Video — "The Normal Distribution: Crash Course Statistics #19"
🔗 https://www.youtube.com/watch?v=rBjft49MAO8
Why it earns the click: the liveliest tour of why the bell curve shows up everywhere and how its mean and standard deviation shape it — pure Segment 2.
⏱ ~12 min

② The 68–95–99.7 (Empirical) Rule

Maps to Lecture Segment 3. Memorize the three numbers once: 68% within 1σ, 95% within 2σ, 99.7% within 3σ — and the tails (16% / 2.5% / 0.15% on each side) are where "unusual" lives.

Reading — "The Empirical Rule (68-95-99.7) | Definition & Examples" (Scribbr)
🔗 https://www.scribbr.com/statistics/empirical-rule/
Why it's assigned: walks the rule and its tail percentages on worked bell-curve examples — the same "draw the ruler, read the bands" move we practiced.
⏱ ~6 min

Video — "Normal distribution: empirical rule" (Khan Academy)
🔗 https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data/normal-distributions-library/v/ck12-org-normal-distribution-problems-empirical-rule
Why it earns the click: a short worked example of applying 68–95–99.7 to a real variable — exactly the Think-Pair-Share we ran in class.
⏱ ~5 min

③ Standardizing · the z-score

Maps to Lecture Segment 5. The recipe: z = (value − mean) ÷ standard deviation. Positive is above the mean, negative below — and z strips the units so any two values can be compared.

Reading — "Z-Score | Definition, Formula & Calculation" (Scribbr)
🔗 https://www.scribbr.com/statistics/z-score/
Why it's assigned: nails the z-score formula and its meaning, and shows the "compare across different distributions" move — the punchline of our height-vs-price example.
⏱ ~7 min

Reading — "Z-scores review" (Khan Academy, article)
🔗 https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data/z-scores/a/z-scores-review
Why it's assigned: a compact review of computing and interpreting a z-score, with the "how many SDs from the mean?" framing we used all week.
⏱ ~5 min

④ From a z-score to an Area / Percentile · Assessing Normality

Maps to Lecture Segments 6–7. Three moves are the whole toolkit: left area = read it; right = 1 − left; between = (left of the bigger) − (left of the smaller). And only trust the bell when the data are roughly normal.

Reading — "The Standard Normal Distribution | Calculator, Examples & Uses" (Scribbr)
🔗 https://www.scribbr.com/statistics/standard-normal-distribution/
Why it's assigned: connects the z-score to the area/percentile under the standard normal — turning "two SDs above the mean" into "the 97.72nd percentile," exactly our Segment-6 work.
⏱ ~7 min

Video — "Z-Scores and Percentiles: Crash Course Statistics #18"
🔗 https://www.youtube.com/watch?v=uAxyI_XfqXk
Why it earns the click: shows how a z-score becomes a percentile and why that lets you compare values measured on totally different scales — the "great equalizer" idea from Segment 5.
⏱ ~11 min

Optional one-stop reference (free online text)

If you'd like one optional reference to skim all term, OpenIntro Statistics keeps its full text and per-section videos free to read online. Chapter 4 ("Distributions"), Section 4.1 ("Normal distribution") covers everything in this week — the bell curve, the empirical rule, z-scores, and normal-curve areas.
🔗 https://www.openintro.org/book/os/
Why it's here: a reputable, currently-available reference you can return to in later weeks — entirely optional this week. (It also has a free online normal distribution calculator under Chapter 4 if you want to check your by-hand answers.)

Pick-one quick path (≈15 min total)

In a hurry? Do exactly these four and you'll be ready for the quiz:
1. Read Normal Distribution (group ①).
2. Read The Empirical Rule (68-95-99.7) (group ②).
3. Read Z-Score (group ③).
4. Watch Crash Course #18 — Z-Scores and Percentiles (group ④).

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.