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.
Open →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 →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 →Core Formulas
The essential statistics and probability 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
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Common Questions
What is a p-value?
A p-value is the probability of observing data at least as extreme as the sample, assuming the null hypothesis is true. A small p-value (commonly below 0.05) is evidence against the null hypothesis and supports rejecting it.
What does a confidence interval represent?
A 95% confidence interval means that if you repeated the sampling procedure many times, about 95% of the intervals constructed would contain the true population parameter. It is not a probability statement about a single interval after it is computed.