AP Statistics
Advanced Placement Statistics covering data analysis, probability, and statistical inference.
Advanced Topics
Probability Distributions
Understanding Distributions
A probability distribution shows all possible outcomes and their probabilities.
Common Distributions
- Binomial distribution: Counts successes in a fixed number of trials.
- Normal distribution: The famous 'bell curve', important in many natural phenomena.
The Normal Distribution
- Symmetrical and centered at the mean.
- About 68% of values fall within one standard deviation of the mean.
\[ Z = \frac{X - \mu}{\sigma} \]
Applications
Probability distributions help with making predictions, setting quality controls, and analyzing risks.
Examples
A company uses the normal distribution to assess product quality.
A sports analyst models the number of goals in games with a binomial distribution.
In a Nutshell
Probability distributions let us model and predict real-world randomness.