Statistics Topic
Statistics and Probability
Analyze data, quantify uncertainty, and draw conclusions from evidence. From basic probability rules to hypothesis testing and confidence intervals.
Learning Path
Normal Distribution Poster
Visual guide to the normal distribution, Z-scores, the 68-95-99.7 rule, and how to find probabilities using the standard bell curve.
View Poster →Probability Distributions Explorer
Explore normal, binomial, Poisson, and uniform distributions. Visualize PDF and CDF plots, compute probabilities with draggable bounds, and find inverse values.
Open Tool →Hypothesis Testing Lab
Set up a one-sample z-test with population mean, sample mean, standard deviation, and sample size. Compute the z-statistic, p-value, and decision to reject or fail to reject.
Open Lab →Core Formulas
- Z-score: z = (x - mu) / sigma
- 68% within 1 sigma, 95% within 2 sigma
- P(A or B) = P(A) + P(B) - P(A and B)
- Confidence interval: x-bar +/- z*(sigma/sqrt(n))
- p-value: probability of data given H0 is true
More Resources
Normal Distribution and Z-Score Explorer
Interactive bell curve with shaded probability regions. Convert between raw scores and Z-scores with numerical integration and probability display.
Open Tool →Bootstrap and Confidence Interval Lab
Draw bootstrap resamples to build confidence intervals. Run coverage simulations to verify that 95% CIs capture the true parameter 95% of the time.
Open Lab →Monte Carlo Simulation Lab
Estimate pi with dart-throwing, solve the birthday problem, drop Buffon's needle, and trace random walks. Watch convergence plots approach true values over thousands of trials.
Open Lab →Probability Distributions Cheat Sheet
Binomial, normal, and Poisson distributions with formulas, parameters, and when to use each.
View Cheat Sheet →