In a normal distribution, 95% of the data lies within how many standard deviations of the mean?

2 is correct because of the empirical (68–95–99.7) rule for normal distributions: about 68% of data fall within 1 standard deviation (σ) of the mean, about 95% within 2σ, and about 99.7% within 3σ. More precisely, 95% corresponds to z-scores of about ±1.96, which is very close to 2. So 1 is too narrow (~68%), and 3 or 4 are wider than needed. Why it matters: Many real-world measurements approximate the bell curve, and means of samples are often modeled as normal by the Central Limit Theorem. That’s why 95% confidence intervals are frequently reported as mean ± 1.96 × standard error. Memory tip: “1–2–3 goes 68–95–99.7” or “Two sigma ≈ 95%.”