Advanced Topics
In a nutshell: Probability distributions let us model and predict real-world randomness.
## 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.
Key terms
- Standard deviation
- A measure of how much data varies from the mean.
- Normal distribution
- A symmetric, bell-shaped distribution important in statistics.