References: The bell curve: the normal distribution

Source material

Source curriculum (structural mirror, cited as further study):
• Khan Academy, "Modeling data distributions" (Statistics & Probability)
  Author: Sal Khan and the Khan Academy team
  Unit page: https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data
  License: CC BY-NC-SA 4.0
Clawdemy's lessons are original prose that follows the pedagogical arc of this
unit. We do not embed, reproduce, or transcribe Khan's text or videos; we link
out to the relevant unit as recommended further study. The non-commercial
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Source-scope note: this lesson mirrors Khan's "Modeling data distributions"
unit (density curves, the normal distribution, z-scores, the empirical rule)
and restates it in Clawdemy's voice with original examples (test scores,
heights). The reason the normal is so common (sums and averages tending to
normal) is previewed here and developed fully in Track 9's central-limit-theorem
lesson. The AI connections (standardization as z-scores, Gaussian noise and
initialization, outlier detection) are Clawdemy framing. Exact per-unit URLs
are verified at promotion.

Read this next

• Khan Academy: Modeling data distributions by Sal Khan and the Khan Academy team. The full unit this lesson mirrors, with videos and practice on density curves, the normal distribution, z-scores, and the empirical rule, free and CC-licensed. The place to drill z-score and percentile problems.

Going deeper

A short, durable list. Both are free.

• Khan Academy, “Summarizing quantitative data” (within the course above). Revisit standardization there; the z-score in this lesson is the same calculation, now used to read positions on a normal curve.
• Khan Academy, “Sampling distributions” (within the course above). The bridge to why the normal is everywhere: the distribution of a sample average is approximately normal even when the data is not. This is Track 9’s central-limit-theorem lesson.

Adjacent topics

Where this sits inside this track.

• Random variables and expected value. The previous lesson. The mean and standard deviation that define a normal are the expected value and spread from there, now describing a continuous bell.
• Counts and trials: the binomial distribution. The next lesson. It returns to discrete random variables to model the number of successes in a fixed number of trials.
• From sample to population: sampling and the central limit theorem. Phase 4. The reason the normal shows up so often: averages of many independent things tend toward it.