🎓 📊 Statistics Course: The Normal Distribution
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Introductory presentation on the normal distribution with practical examples, plots, and theoretical foundations applied to Statistics.
← Statistics Courses · ← Statistics Section
🚀 Quick Access to the Parts
- 🎯 👉 Part 1 — Introduction to the Normal Distribution
- 🎯 👉 Part 2 — z-Score and the Z Table
- 🎯 👉 Part 3 — Plots, CLT, and Approximate Normality
🎯 Course Objectives
Note
By the end of the course, you will be able to:
- ✅ Understand the concepts of population, sample, and random variables;
- 📊 Grasp the role of the probability density function (PDF);
- 📐 Identify the features of the standard normal curve (\(\mu=0\), \(\sigma=1\));
- 📈 Apply the Empirical Rule (68–95–99.7%);
- 🧮 Compute probabilities with Excel, R, and Python;
- 🔁 Use the z-score for standardization and comparisons;
- 📉 Generate/interpret normal-distribution plots in real contexts;
- 🧠 Relate the normal distribution to the CLT and LLN;
- 🔍 Recognize approximate normality via histograms, Q–Q plots, and exploratory checks.
Tip
Recommended prerequisites: notions of algebra and functions; mean, standard deviation, and chart reading. Target audience: students and professionals who need to interpret data based on probabilistic models.
📚 Syllabus — Part 1: Introduction to the Normal Distribution
🎯 👉 Open Part 1
- Fundamental concepts: population, sample, and variables
- Discrete vs. continuous variables
- Distributions and PDF
- Definition, importance, and properties of the normal distribution
- Real-world examples
- Standard curve (\(\mu=0\), \(\sigma=1\)), symmetry, and shape
- PDF formula, area as probability, effect of \(\mu\) and \(\sigma\)
- Empirical Rule (68–95–99.7%) — interpretation and applications
- Visualizations with Python and R
📚 Syllabus — Part 2: z-Score and the Z Table
🎯 👉 Open Part 2
- Definition, formula, and interpretation of the z-score
- Comparing values across different distributions
- Case study: probability of IQ > 136
- Reading the Z Table (cumulative \(P(Z<z)\)) and shaded areas
- Calculations in Excel (
NORM.S.DIST,NORM.S.INV) and R (pnorm,qnorm,dnorm) - Guided exercises
📚 Syllabus — Part 3: Plots, CLT, and Approximate Normality
🎯 👉 Open Part 3
- Histograms and interpretation
- Q–Q plots: what they are and how to read them
- What “approximately normal” means
- Examples of variables with/without normality
- LLN (Law of Large Numbers) — intuition and practical implications
- CLT (Central Limit Theorem) — sample means and computational examples
📖 References
Important
- Schmuller, Joseph. Statistical Analysis with Excel® For Dummies®, 5th ed. Wiley, 2016.
- Schmuller, Joseph. Análise Estatística com R Para Leigos, 2nd ed. Alta Books (Portuguese edition), 2021.
- Levine, D. M.; Stephan, D.; Szabat, K. A. Statistics for Managers Using Microsoft Excel, 8th ed. Pearson, 2017.
- Morettin, L. G. Estatística Básica: Probabilidade e Inferência, 7th ed. Pearson, 2017.
- Morettin, P. A.; Bussab, W. O. Estatística Básica, 10th ed. SaraivaUni, 2023.
🔗 Quick Access (again)
- 🎯 👉 Part 1 — Introduction to the Normal Distribution
- 🎯 👉 Part 2 — z-Score and the Z Table
- 🎯 👉 Part 3 — Plots, CLT, and Approximate Normality
← Statistics Courses · ← Statistics Section
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