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ap statistics - normal distribution & z-scores

originally streamed in 2019 with Josh ArgoTeacher
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Learn normal distribution and z-scores for AP Statistics. This review covers the empirical rule, probability calculations, and Central Limit Theorem—all critical for your AP Stats exam. The normal curve is one of the most tested concepts in AP Stati ...more

curriculum note

This video references the 2020 AP Statistics exam format, which had modified time constraints and calculator restrictions due to COVID-19. The current exam format and calculator policy may differ.

covered in this stream

units
Unit 1 – Exploring One–Variable DataUnit 5 – Sampling Distributions
topics
1.10 The Normal DistributionDescribing Location in a Distribution5.2 The Normal Distribution, Revisited5.3 The Central Limit Theorem5.5 Sampling Distributions for Sample Proportions5.7 Sampling Distributions for Sample Means

timestamps

  • 0:00

    Importance of Normal Distribution

  • 0:31

    Percentiles and Normal Curve

  • 1:34

    Empirical Rule Explanation

  • 2:36

    Checking for Outliers

  • 3:39

    IQ Scores Example

  • 4:42

    Standard Normal Curve

  • 5:44

    Z-Scores Introduction

  • 6:15

    Comparing ACT and SAT

  • 7:48

    Interpreting Z-Scores

  • 8:50

    Z-Score Formula

  • 9:54

    Grades Comparison Example

  • 12:35

    Determining Better Performance

  • 13:37

    Calculating Probabilities

  • 14:39

    Lego Weight Probability

  • 17:21

    Using Z-Score Table

  • 19:30

    Calculator NormalCDF Method

  • 24:55

    Sampling Distributions Overview

  • 26:27

    Proportions and Means Formulas

  • 29:02

    Sampling Distribution Explanation

  • 31:09

    Lego Sample Probability

  • 34:20

    Standard Deviation in Sampling

  • 37:37

    Voting Poll Proportions Example

  • 39:41

    Probability Calculation for Proportions

  • 40:43

    Normal Curve in Inference

  • 42:16

    Balloons House Lifting Example

  • 43:49

    Normal Condition Importance

  • 45:23

    Study Randomization Issue

  • 47:58

    P-Value Interpretation

  • 49:33

    Rejecting Null Hypothesis

  • 50:34

    Final Thoughts and Q&A

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Fiveable

Study Content & Tools

Study GuidesFRQs + AI ScoringAP Essay Grader for StudentsAI Grading for TeachersPractice QuestionsGlossaryScore Calculators

Company

What's New?PricingBulk DiscountsTestimonialsFAQsEmail us

Resources

AP Exam Schedule 2027AP Exam AccommodationsAP ClassesAP ClassroomEasiest AP ClassesHardest AP ClassesAP vs IBAP vs Dual EnrollmentAP vs Honors ClassesAP Scholar Awards

history

🌎 ap world history🇺🇸 ap us history🇪🇺 ap european history

social science

✊🏿 ap african american studies🗳️ ap comparative government🚜 ap human geography💶 ap macroeconomics🤑 ap microeconomics🧠 ap psychology👩🏾‍⚖️ ap us government

english & capstone

✍🏽 ap english language📚 ap english literature🔍 ap research💬 ap seminar

arts

🎨 ap art & design🖼️ ap art history🎵 ap music theory

science

🧬 ap biology🧪 ap chemistry♻️ ap environmental science🎡 ap physics 1🧲 ap physics 2💡 ap physics c: e&m⚙️ ap physics c: mechanics

math & computer science

🧮 ap calculus ab♾️ ap calculus bc📐 ap precalculus📊 ap statistics💻 ap computer science a⌨️ ap computer science p

world languages

🇨🇳 ap chinese🇫🇷 ap french🇩🇪 ap german🇮🇹 ap italian🇯🇵 ap japanese🏛️ ap latin🇪🇸 ap spanish language💃🏽 ap spanish literature

career kickstart

💼 ap business with personal finance🔒 ap cybersecurity

go beyond AP

high school exams

✏️ PSAT🎓 Digital SAT🎒 ACT

honors classes

🍬 honors algebra II🫀 honors anatomy🐇 honors biology👩🏽‍🔬 honors chemistry💲 honors economics📐 honors geometry⚾️ honors physics📏 honors pre-calculus📊 honors statistics🗳️ honors us government🇺🇸 honors us history🌎 honors world history

college classes

👩🏽‍🎤 arts👔 business🎤 communications🏗️ engineering📓 humanities➗ math🧑🏽‍🔬 science💶 social science

hs classes

🏛️ alabama history⛰️ appalachian studies🌴 california history🌍 earth science🌐 ethnic studies🐊 florida history🍑 georgia history🌎 global studies🌺 hawaiian studies📰 journalism🪶 native american studies🌵 new mexico history🤠 oklahoma history⚗️ physical science🎙️ speech and debate🤝 texas government🤠 texas history🌲 washington state history🕊️ world religions
RefundsTermsPrivacyCCPAAI TransparencySchool Data Privacy

© 2026 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.