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.

Key Terms

Standard deviation
A measure of how much data varies from the mean.
Normal distribution
A symmetric, bell-shaped distribution important in statistics.
Probability Distributions - AP Statistics Content | Practice Hub