AP Statistics

Advanced Placement Statistics covering data analysis, probability, and statistical inference.

Advanced Topics

Probability Distributions

Patterns in Randomness

A probability distribution shows all possible outcomes of a random variable and how likely they are. Two important types are discrete (countable outcomes) and continuous (any value in a range).

Common Distributions

  • Binomial Distribution: Number of successes in a series of yes/no trials.
  • Normal Distribution: The famous bell-shaped curve, seen in heights, test scores, etc.

The normal distribution is described by its mean (\( \mu \)) and standard deviation (\( \sigma \)). Many real-world variables roughly follow this pattern!

Why Distributions Matter

Understanding distributions helps us predict outcomes, spot outliers, and make better decisions.

Examples

  • A casino uses the binomial distribution to calculate the odds of winning a game.

  • SAT scores are often modeled using a normal distribution.

In a Nutshell

Probability distributions describe the expected outcomes and their likelihood.