Chapter 7.1, Problem 30E

Find the area under the standard normal curve that lies outside the interval between

1. $z=-1.11$ and $z=3.21$
2. $z=-1.93$ and $z=0.59$
3. $z=0.46$ and $z=1.75$
4. $z=-2.73$ and $z=-1.39$

To determine

To find area outside the -1.11 and 3.21

Answer to Problem 30E

Area outside the -1.11 and 3.21 is 0.1342

Explanation of Solution

Given:

  $\begin{array}{l}{z}_1=-1.11\\ z_2=3.21\end{array}$

Shaded region is outside of above z-scores

That is to find $P\left(Z<-1.11\right)+P\left(Z>3.21\right)$

Calculation:

Using standard normal table,

  $\begin{array}{l}P\left(Z<-1.11\right)=0.1335\hfill \\ P\left(Z<3.21\right)=0.9993\hfill \\ So,\hfill \\ P\left(Z>3.21\right)=1–0.9993=0.0007\hfill \\ Therefore,\hfill \\ P\left(Z<-1.11\right)+P\left(Z>3.21\right)=0.1335+0.0007=0.1342\hfill \end{array}$

To determine

To find area outside the -1.93 and 0.59

Answer to Problem 30E

Area outside the -1.93 and 0.59 is 0.3044

Explanation of Solution

Given:

  $\begin{array}{l}{z}_1=-1.93\\ z_2=0.59\end{array}$

Shaded region is outside of above z-scores

That is to find $P\left(Z<-1.93\right)+P\left(Z>0.59\right)$

Calculation:

Using standard normal table,

  $\begin{array}{l}P\left(Z<-1.93\right)=0.0268\hfill \\ P\left(Z<0.59\right)=0.7224\hfill \\ So,\hfill \\ P\left(Z>0.59\right)=1–0.7224=0.2776\hfill \\ Therefore,\hfill \\ P\left(Z<-1.93\right)+P\left(Z>0.59\right)=0.0268+0.2776=0.3044\hfill \end{array}$

To determine

To find area outside the 0.46 and 1.75

Answer to Problem 30E

Area outside the 0.46 and 1.75 is 0.7173

Explanation of Solution

Given:

  $\begin{array}{l}{z}_1=0.46\\ z_2=1.75\end{array}$

Shaded region is outside of above z-scores

That is to find $P\left(Z<0.46\right)+P\left(Z>1.75\right)$

Calculation:

Using standard normal table,

  $\begin{array}{l}P\left(Z<0.46\right)=0.6772\hfill \\ P\left(Z<1.75\right)=0.9599\hfill \\ So,\hfill \\ P\left(Z>1.75\right)=1–0.9599=0.0401\hfill \\ Therefore,\hfill \\ P\left(Z<0.46\right)+P\left(Z>1.75\right)=0.6772+0.0401=0.7173\hfill \end{array}$

To determine

To find area outside the -2.73 and -1.39

Answer to Problem 30E

Area outside the -2.73 and -1.39 is 0.9209

Explanation of Solution

Given:

  $\begin{array}{l}{z}_1=-2.73\\ z_2=-1.39\end{array}$

Shaded region is outside of above z-scores

That is to find $P\left(Z<-2.73\right)+P\left(Z>-1.39\right)$

Calculation:

Using standard normal table,

  $\begin{array}{l}P\left(Z<-2.73\right)=0.0032\hfill \\ P\left(Z<-1.39\right)=0.0823\hfill \\ So,\hfill \\ P\left(Z>-1.39\right)=1–0.0823=0.9177\hfill \\ Therefore,\hfill \\ P\left(Z<-2.73\right)+P\left(Z>-1.39\right)=0.0032+0.9177=0.9209\hfill \end{array}$