Normal Density Functions The family of bell-shaped curves

occurs in probability and statistics, where it is called the normal density function. The constant μ is called the mean and the positive constant σ is called the standard deviation. For simplicity, let’s scale the function so as to remove the factor 1/(σ√2π) and let’s analyze the special case where μ = 0. So we study the function

f(x) = e^–x2/(2σ2)

(a) Find the asymptote, maximum value, and inflection points of f .

(b) What role does σ play in the shape of the curve?

(c) Illustrate by graphing four members of this family on the same screen.

Transcribed Image Text:

y = 1 σ√√2TT e-(x-μ)²/(20²)