Course: Introduction to Statistics (18-week generic edition)
Module: Week 8 of 18 · planned around two ~75-minute sessions
Objective covered: Objective 5 (normal-distribution portion) — use the normal model to compute and interpret proportions and percentiles.

This file holds two pieces: (A) the Module 8 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. All timing is relative — "start of Week 8," "end of Week 8" — and maps onto real dates when the adopting instructor sets the term calendar.

(A) Module 8 Overview — Start Here

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.

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.

(B) Welcome Announcement — Module 8

Release setting: drips at the start of Week 8 (offset = 0 days from module start) — not before. If your platform won't preserve the scheduled release on import, post it as a draft labeled "Release: start of Week 8."

Subject: Week 8 — the most famous curve in statistics (and your midterm roadmap)

Hi everyone,

Remember last week's binomial histograms — how the bars kept arranging themselves into the same bell silhouette? That was a preview. This week we meet the curve itself: the normal distribution, drawn completely by just two numbers, and able to turn "how far from typical?" into an exact percentage. What percent of batteries outlast the warranty? How unusual is a 70-inch woman — and is she relatively taller than a 74-inch man? By the end of the week, those are one z-score and one table lookup away.

Three things not to miss:
1. Chapter 8 is your primary reading — it carries the friendly z-table you'll use everywhere this week. Start there.
2. Data Lab 8 puts the week's big judgment call — is the bell actually there? — to the test on our penguins. Spoiler: which penguins you pool changes the answer. The Discussion ("Designed for the Middle") wants your initial post two days before the week ends.
3. Midterm heads-up, calmly: next week's midterm covers Weeks 1–8 — and it's a low-stakes checkpoint (5%, 50 multiple-choice, closed to AI). The study guide, practice exam, and exam-prep tutorial are all in the Week 9 module. This week's lecture closes with the review roadmap, so you'll walk in with the whole first half organized as one story.

One habit to bring: before any table lookup, sketch the bell and shade the region you want. Ten seconds of drawing prevents the classic wrong-tail error — and this week you'll also get to catch your chatbot misquoting a z-table from memory. The tool drafts; you judge.

Open the Start Here / Module Overview page first — it lays out everything in order with due points. See you in the course!