AP Statistics / Unit 2: Probability, Random Variables, and Probability Distributions
2.11 The Normal Distribution
Notes
A normal distribution is symmetric and bell-shaped, described by $\mu$ and $\sigma$.
- Empirical rule: about 68%, 95% and 99.7% within 1, 2 and 3 standard deviations.
- z-score: $\displaystyle z=\frac{x-\mu}{\sigma}$.
Practice
Heights: $\mu=66$, $\sigma=3$. About what percent are between 60 and 72?
Within 2 standard deviations.
The z-score of 75 when $\mu=60$, $\sigma=5$:
$\displaystyle \frac{75-60}{5}$.
A z-score of $-1$ means the value is:
z measures standard deviations from the mean.
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