Topic 5 · Interactive tool
Normal Distribution Explorer
Set the mean and the standard deviation, then see what the empirical rule says: how much of the data sits within one, two or three standard deviations of the mean.
Normal distribution · empirical rule
68% within μ ± 1σ · 95% within μ ± 2σ · 99.7% within μ ± 3σ
With μ = 100 and σ = 15, the middle 95% of values fall between 70 and 130.about 15.87% of values fall below X = 85.
P(X < x)
15.87%
area to the left of X
P(X > x)
84.13%
area to the right of X
Z-score of X
−1.000
how many σ from μ
Empirical rule
68 / 95 / 99.7
% within ±1σ / ±2σ / ±3σ
Find U, V and W
Mean (μ) 100
−50250
Standard deviation (σ) 15
150
Cutoff X 85
−100300
Scenarios