12. Consider the normal curves that have the parameters $\mu =1.5$and $\sigma =3;\mu =1.5$and $\sigma =6.2;\mu =-2.7$and $\sigma =3;\mu =0$and$\sigma =1.$

a. Which curve has the largest spread?

b. Which curves are centered at the same place?

c. Which curves have the same spread?

d. Which curve is centered farthest to the left?

e. Which curve is the standard normal curve?$\sigma$

Consider the normal curve with parameters:

$\begin{array}{rl}-\mu & =1.5\text{and}\sigma =3\\ -\mu & =1.5\text{and}\sigma =6.2\\ -\mu & =-2.7\text{and}\sigma =3\\ -\mu & =0\text{and}\sigma =1\end{array}$

The standard deviation $\sigma$of the curve with the biggest spread is the largest. The curve having the largest spread among the given curves is:

$\mu =1.5$and$\sigma =6.2$

Consider the normal curve with parameters:

$\begin{array}{rl}-\mu & =1.5\text{and}\sigma =3\\ -\mu & =1.5\text{and}\sigma =6.2\\ -\mu & =-2.7\text{and}\sigma =3\\ -\mu & =0\text{and}\sigma =1\end{array}$

The mean $\mu$of curves with the same centers is the same. The curves that are centered in the same position among the given curves are:

$\mu =1.5$and $\sigma =3$and $\mu =1.5$and$\sigma =6.2$

Consider the normal curve with parameters:

$\begin{array}{rl}-\mu & =1.5\text{and}\sigma =3\\ -\mu & =1.5\text{and}\sigma =6.2\\ -\mu & =-2.7\text{and}\sigma =3\\ -\mu & =0\text{and}\sigma =1\end{array}$

The standard deviation $\sigma$of curves with similar spreads is the same. The curves with the same spreads among the given curves are:

$\mu =1.5\text{and}\sigma =3\text{and}\mu =-2.7\text{and}\sigma =3$

Consider the normal curve with parameters

$\begin{array}{rl}-\mu & =1.5\text{and}\sigma =3\\ -\mu & =1.5\text{and}\sigma =6.2\\ -\mu & =-2.7\text{and}\sigma =3\\ -\mu & =0\text{and}\sigma =1\end{array}$

When the mean is smallest, the curve will be centered to the left. From the given curves, the curve that is centered to the left is:

$\mu =-2.7\text{and}\sigma =3$

Consider the normal curve with parameters:

$\begin{array}{rl}-\mu & =1.5\text{and}\sigma =3\\ -\mu & =1.5\text{and}\sigma =6.2\\ -\mu & =-2.7\text{and}\sigma =3\\ -\mu & =0\text{and}\sigma =1\end{array}$

For each curve, the mean is $\mu =0$ and the standard deviation is $\sigma =1$. For each curve, the standard normal curve is:

$\mu =0\text{and}\sigma =1$