A normal curve distributes total probability one over an unbounded axis.
WHAT HAPPENS IF…What probability lies within one standard deviation of the mean?
Interactive exploration
Loading the mathematical model…
Connect the picture to the ideaf(x)=σ2π1e−(x−μ)2/(2σ2),σ>0
Standardizing z=(x−μ)/σ converts interval probabilities to the standard normal scale. Increasing σ stretches the density horizontally and lowers its peak, preserving total area. The displayed interval probability uses Simpson quadrature, not a finite-sample frequency.
A detail that matters
A density value is not the probability of one exact continuous outcome.