Question

Sketch the normal distribution with

$$\begin{gathered} \left(a\right)\mu =3;\sigma =3 \\ \left(b\right)\mu =1;\sigma =3 \\ \left(c\right)\mu =3;\sigma =1 \end{gathered}$$

Short answer

(a) The normal distribution with $\mu =3;\sigma =3$is:

(b) The normal distribution with $\mu =1;\sigma =3$is:

(c) The normal distribution with role="math" localid="1652507031330" $\mu =3;\sigma =1$is:

Step-by-step solution

Part (a) Step 1. Given Information.

$\mu =3;\sigma =3$

Part (a) Step 2. Sketch the normal distribution.

The normal distribution is:

Part (b) Step 1. Sketch the normal distribution.

The normal distribution with $\mu =1;\sigma =3$is:

Part (b) Step 1. Sketch the normal distribution.

The normal istribution with $\mu =3;\sigma =1$is:

Part (c) Step 2. Sketch all three distributions.

Sketch all the distribution in a single graph: