{"id":"normal-distribution","domain":"probability-statistics","type":"Concept","title":"Normal Distribution","slug":"normal-distribution","url":"/mathematics/probability-statistics/normal-distribution/","summary":"The symmetric bell curve, arising from the Central Limit Theorem. Also called Gaussian distribution. Determined by mean and standard deviation.","formal_definition":"f(x) = (1/sigma*sqrt(2pi)) * e^(-(x-mu)^2/2sigma^2)","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Feller, W. (1968/1971). An Introduction to Probability Theory. Vols 1-2, 3rd ed."},{"tier":1,"citation":"Billingsley, P. (1995). Probability and Measure. 3rd ed."},{"tier":2,"citation":"Stigler, S.M. (1986). The History of Statistics. Harvard University Press."},{"tier":3,"citation":"Salsburg, D. (2001). The Lady Tasting Tea. W.H. Freeman."}],"relationships":[{"type":"built_from","target":"random-variable","label":"Random Variable"},{"type":"uses","target":"irrational-number","label":"Irrational Number — e, π"},{"type":"uses","target":"matrix","label":"Matrix — multivariate covariance"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.7"}