Title: Week 8 Overview — Start Here
Course: Introduction to Statistics (18-Week Generic Edition)

Welcome to Week 8: The Normal 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.

Last week the binomial's bars kept forming the same silhouette — a bell. This week we name that curve and put it to work. The normal distribution is described by just two numbers (a mean and an SD), and it performs a genuinely useful trick: it converts how far from typical into an exact percentage — in both directions. Heights, machine fill volumes, battery lifetimes: one curve, everywhere. This is also the week the course's first half clicks together — the midterm lands next week, and this module kicks off the review.

The week's big question

"One bell-shaped curve keeps showing up — in heights, lifetimes, and fill volumes. How do we use it to turn 'how far from typical?' into an exact percentage?"

By the end of the week you'll answer questions like: what percent of batteries outlast 106 hours? How unusual is a 70-inch woman — and is she relatively taller than a 74-inch man? What warranty mileage should a tire company advertise? And the professional's question before all of those: is the bell actually there?

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.

- [ ] Read a density curve — total area 1, and area between two values = the proportion of the data there ("area, not height").
- [ ] Apply the empirical rule — about 68% of a normal model within 1 SD, 95% within 2, 99.7% within 3 (the only numbers you memorize this week).
- [ ] Compute and interpret a z-score — z = (x − μ)/σ — and use z to compare values from different distributions on one ruler.
- [ ] Run forward and inverse normal calculations — value → percent with the friendly z-table (below/above/between), and percent → value with x = μ + z·σ — plus the spreadsheet versions =NORM.DIST() and =NORM.INV().
- [ ] Assess normality before trusting the model — histogram shape, the actual 68/95 check, and a skew/outlier hunt.

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 8 — the module's primary reading; the friendly z-table lives in its Section 4 | Chapter (ungraded prep) | Early in the week
2 | Skim the slides (Deck 8) and the Week 8 lecture outline; browse the Readings & Resources links that interest you | Prep (ungraded) | Alongside class
3 | Lecture Tutorial 8 — work the week's ideas with your chatbot (it gets the z-table too), then submit the share link + Completion Summary | Tutorial · graded (Lecture tutorials, 20% group) | End of Week 8
4 | Practice exercises — quick reps with the AI coach | Practice · ungraded | Before the quiz (recommended)
5 | Data Lab 8 — "Is the Bell Really There? The Penguins Meet the Normal Model" — run the week's three normality checks on real penguin data, pooled vs. one species | Data lab · graded (Data labs, 15% group) | End of Week 8
6 | Quiz 8 — density curves, empirical rule, z-scores, forward & inverse calculations, assessing normality | Quiz · graded (Quizzes, 15% group) · closed to AI | End of Week 8
7 | Discussion 8 — "Designed for the Middle" — debate who bell-curve design leaves out, with your chatbot as sparring partner; post the AI summary + chat link | Discussion · graded (Discussions, 15% group) | Initial post two days before week's end; replies by end of Week 8
8 | Assignment 8 — "The Bell Curve at Work" — four AI-coached problems (batteries, heights, bottling, tire warranties); submit the report (score on line 1) + chat link | Assignment · graded (Assignments, 25% group) | End of Week 8

Heads-up on the AI work: in this course the chatbot drafts, and you judge. This week's signature catch: chatbots quoting z-tables from memory — they drift by a digit or invent precision. Your tutorial, lab, and assignment all embed the course's friendly z-table precisely so you can check the machine against it.

Midterm heads-up — read this even if you read nothing else

Next week is Midterm Week. Here's everything you need to know, calmly:

- The midterm covers Weeks 1–8 — everything through this module. It's 50 multiple-choice questions, closed to AI, and it's a low-stakes checkpoint: 5% of the grade. Your weekly work remains the grade engine.
- The Week 9 module carries the full exam bundle: a study guide, a practice exam, and an exam-prep tutorial (that tutorial is next week's graded tutorial). Start with the study guide's self-diagnosis — not with rereading everything.
- The review starts now, gently: this module's lecture closes with the review roadmap — the whole first half as one story (get data honestly → describe it → quantify chance → model it). Week 8's normal model is the last piece and the bridge to everything after.
- You only memorize 68–95–99.7 and the z recipe; any table values the midterm needs are provided.

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

- Sketch and shade before every lookup. Draw the bell, mark the mean, shade the region — then ask "should the answer be more or less than half?" That one habit kills the wrong-tail error that costs the most points.
- Memorize exactly three numbers. 68 – 95 – 99.7, glued to 1 – 2 – 3 SDs. Everything else is the table or =NORM.DIST().
- Say z-scores in words. "z = −1.5" is "one and a half SDs below the mean." Words catch the sign errors that digits hide — and remember, negative z is a direction, not a defect.
- Password-protect the rule. IF bell-shaped, THEN 68–95–99.7. Check the shape first — the lab shows you exactly how, and why a pooled mixture can fool one check.
- Percentile ≠ percent score. The 84th percentile means 84% sit below you (z = 1 territory) — nobody "scored 84%."

You've built every tool this week needs: the SD ruler from Week 3 and the model habit from Weeks 5–7. This week they merge — come ready to turn distances into percentages.