Section 2 · Lecture 07 · Normal Distribution
Every Normal distribution is determined by two numbers. The mean μ sets its location and the standard deviation σ sets its width. Because the total area under the curve must always equal 1, σ also sets its height.
Compare curves
Presets
Mean = median = mode
Peak height, f(μ)
Total area under the curve
Working it out
Compared with the reference N(0, 1)
μ does not appear in the peak height, so sliding the curve left or right never changes its shape. Only σ changes the height: doubling σ doubles the width and halves the peak, which keeps the total area equal to 1.