Normal Distribution
A bell-shaped, symmetric distribution for real‑valued variables. The mean sets the center and the standard deviation controls the spread.
Probability Density FunctionPDF = f(x)
Cumulative Distribution FunctionCDF = F(x)
Probability in an Interval
Compute the probability that X falls between two values. For continuous distributions, this is the shaded area under the PDF (≤ vs < doesn't matter).
P(a ≤ X ≤ b)
Quantiles (Inverse CDF)
Pick a probability p and read the corresponding quantile xₚ where F(xₚ) = p.
Quantile xₚ (where F(xₚ) = p)
In Normal Distribution, selected probability p: 0.9500 (95.00%)
Parameters
Adjust the parameters and (optionally) add up to 3 curves to compare different settings side‑by‑side.
0 curves shown
Estimating parameters from data
If you’re fitting this distribution to observed data, these are common plug‑in estimates you can start with.
Mean (μ)
Estimate μ with the sample mean: add all observations and divide by the sample size.
Standard Deviation (σ)
Estimate σ with the sample standard deviation. In practice you may see n−1 (unbiased) or n (population) in the denominator depending on context.