Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Module: Week 9 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 5 — Use normal distributions to reason about variability.

This file holds two pieces: (A) the Module 9 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 9 meeting Tue Oct 27 and Thu Oct 29, and end-of-week work due Sunday Nov 1, 11:59 p.m. Adjust the day-of-week and times to match your section.

(A) Module 9 Overview — Start Here

Welcome to Week 9: 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.

Welcome back from the midterm — this week we start building the machinery the second half of the course runs on. Here's the whole idea in one question: is a test score of 80 good? You can't say, until you know the world it came from — the average and the spread. This week we build the most famous "world" in statistics, the bell curve, and a single tool — the z-score — that turns any value into one honest sentence: how many standard deviations from average am I, and how unusual is that? By Friday you'll take a score, a height, a price, or a battery's lifespan and report exactly how unusual it is, as a percentile, from nothing but the mean, the standard deviation, and a small table.

The week's big question

"When a value comes from a bell-shaped world, how unusual is it — and how do we put a number on that?"

By Friday you'll be able to look at any value from a roughly normal distribution and place it precisely: read whole bands off the curve with the 68–95–99.7 rule, standardize it into a z-score, and turn that z-score into an area or percentile using a supplied table.

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 week's graded work.

• [ ] Read a density curve — know that the total area under it is 1, so any area is a proportion (the share of data there), and that the mean splits a normal curve into two equal halves.
• [ ] Apply the 68–95–99.7 (empirical) rule — about 68% of data within 1 SD of the mean, 95% within 2, 99.7% within 3 — and find the tail percentages (16% / 2.5% / 0.15% on each side).
• [ ] Standardize any value into a z-score — z = (value − mean) ÷ SD — and say in plain words what it means (how many SDs from the mean, and on which side). Remember: a negative z just means below the mean.
• [ ] Turn a z-score into an area or percentile using the supplied table — left area = read it (that's the percentile); right = 1 − left; between = (left of the bigger) − (left of the smaller).
• [ ] Judge whether the data are roughly normal — and refuse the bell (and the empirical rule) when the data are clearly skewed or lumpy.

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up: this week's graded set is Quiz 9, Discussion 9, and Assignment 9, plus the weekly Lecture Tutorial. The adaptive assignment lets you keep improving your score by learning, so start early enough to enjoy the re-tries.

Heads-up on the AI work: you'll use a chatbot to draft, and then you judge its work against what we cover in class — and this week, against the table we supply you. Chatbots routinely miss these — they'll answer "68%" when the real area is .8413, or flip the left and right areas, or confidently invent a four-decimal table value. Catching the model is the point.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline — I'd much rather hear from you early.

How to succeed this week

• Lead with the picture, not the formula. Every idea this week is about placing a value in its crowd. Sketch the bell, mark the mean, step out by the standard deviation — then read the answer off the picture.
• Memorize two tiny things. The empirical rule — "68–95–99.7" for 1, 2, 3 SDs — and the z-score recipe: "subtract the mean, divide by the SD."
• Use the one sentence for any z-score. "This value is (z) standard deviations above/below the mean." A negative z isn't an error — it just means below average.
• Three moves cover every area question. Left area = read the table (and that's the percentile). Right = 1 − left. Between = (left of the bigger) − (left of the smaller). Always shade the side the question asks for.
• Don't use the bell when the data aren't one. If a distribution is clearly skewed (incomes, home prices), the empirical rule and percentiles can lie — check for a bell first.
• Treat the chatbot as a smart intern, not an oracle. It drafts an area or a percentile; you check it against the table we hand you. That habit is the whole semester in miniature — and it's literally how Assignment 9 is scored.

You don't need anything from a textbook this week — just the mean, the standard deviation, and the small table built into your materials. Come ready to argue about whether a test score of 80 is actually any good. See you Tuesday.

(B) Welcome Announcement — Module 9

Release setting: post on the module's start day (offset = 0 days), i.e., Tue Oct 27, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Tue Oct 27."

Subject: Week 9 — is a score of 80 actually good? 📈

Hi everyone, and welcome back from the midterm,

Quick question to start: is a test score of 80 good? You honestly can't say — not until you know the average and the spread of the class it came from. An 80 where everyone scored in the 90s is rough; an 80 where the average was 60 is a triumph. That's the whole problem Week 9 solves.

This week — The Normal Distribution — we tackle the big question: When a value comes from a bell-shaped world, how unusual is it — and how do we put a number on it? By Friday you'll take any value — a score, a height, a price, a battery's lifespan — and say exactly how unusual it is, as a percentile, from just the mean, the standard deviation, and a small table.

The one thing not to miss:
1. Assignment 9 (adaptive) — four problems with an approved chatbot (Gemini, Claude, or ChatGPT): apply the 68–95–99.7 rule, compute z-scores, find a percentile from the table we give you, and explain "how unusual" in plain English. It grades you against a rubric, teaches the fixes, and lets you retry for a higher score. Submit the AI's self-scored report plus your chat link. Worth 100 points. Due Sun Nov 1.
2. Quiz 9, Discussion 9, Lecture Tutorial 9, and the practice set also close Sun Nov 1 — the tutorial and practice are the on-ramp; do them first. The discussion ("How unusual is this value?") is a quick AI dialogue you summarize and post, so start early and leave time to reply to classmates.

A callback to earlier weeks: we learned to describe a variable's center and spread. Now we put center and spread to work — one number, the z-score, that says how far any value sits from average and how unusual that is. Remember the week's line: a raw number is a stranger; a z-score is an introduction.

Open the Start Here / Module Overview page first — it lays out everything in order with due dates. Bring your curiosity (and maybe a real test score you've always wondered about) to class on Tuesday.

See you soon,
Prof. Rivera