Understanding Probability Distributions

A probability distribution describes how the probabilities of different outcomes are spread. Understanding distributions is crucial for statistics, data science, and many scientific fields.

Normal Distribution

The normal distribution (bell curve) is the most important distribution in statistics. It is symmetric, with the mean, median, and mode all at the center. The Empirical Rule says that approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.

The Z-score tells you how many standard deviations a value is from the mean. A Z-score of 1.96 corresponds to the 97.5th percentile, which is why 1.96 appears in 95% confidence intervals. Use our Normal Distribution Calculator to find probabilities.

Binomial Distribution

The binomial distribution models the number of successes in n independent trials, each with probability p of success. The formula is P(X=k) = C(n,k) × p^k × (1-p)^(n-k). It applies to coin flips, quality control, medical trials, and many other scenarios.

Use our Binomial Distribution Calculator to compute probabilities quickly.