Work out log normal distribution instantly with clear inputs, formula shown and shareable results.
X is log-normal when ln X is normal, so probabilities are found by standardising the logarithm. The distribution is right-skewed, which is why its mean exceeds its median.
Log-normal CDF
P(X ≤ x) = Φ((ln x − μ)/σ)
Mean and median
mean = e^(μ + σ²/2), median = e^μ
z = (3.2189 − 3)/0.5 = 0.4377, so P(X ≤ 25) ≈ 0.6692. The median is e³ ≈ 20.09 and the mean about 22.76.
Wherever effects multiply rather than add: incomes, particle sizes, stock prices and time-to-failure data.