The normal distribution, G(x), is defined as G(x) = 1 22 e (x) 2 22

The normal distribution, G(x), is defined as G(x) =

1

√

2πσ2 e

−

(x−µ)

2 2σ2

, where σ > 0 and µ are constants. It’s used in a huge variety of applications to describe measurements of just about anything.

a. You can get a rough feel for the function by computing some of the values. Choose any values for µ and σ (make sure that σ > 0) and complete the following table

b. Now use a computer (use any software you like) to plot G(x) for your values of µ and σ. Did your values agree with the shape of the function you see?

c. Plot G(x) for a range of different values of µ and σ. How does the graph change as µ changes? How does the graph change as σ changes?

d. How would you interpret µ and σ scientifically?