Q. 6.68 - Elementary Statistics

Question

Use table $II$ to obtain each shaded area under the standard normal curve

Step-by-Step Solution

Answer

Part $\left(a\right)$: The required area is, $0.9500$.

Part $\left(b\right)$: The required area is, $0.9802$.

Part $\left(c\right)$: The required area is, $0.2006$.

Part $\left(d\right)$: The required area is, $0.1010$.

Part a Step 1 . Given information

Part a Step 2 . Let us find the area for the given diagram.

The area under the standard normal curve that lies between $-1.96$ and $1.96$ equals the area to the left of $1.96$ minus the area to the left of $-1.96$.Standard normal table shows that these latter two areas are $0.9750$ and $0.0250$, respectively. So, the required area is, $0.9750-0.0250=0.9500$.

Part b Step 1 . Given information

Part b Step 2 . Let us find the area for the given diagram.

The area under the standard normal curve that lies between $-2.33$ and $2.33$ equals the area to the left of $2.33$ minus the area to the left of $-2.33$. Standard normal table shows that these latter two areas are $0.9901$ and $0.0099$,respectively. So, the required area is,  $0.9901-0.0099=0.9802$.

Part c Step 1 . Given information

Part c Step 2 . Let us find the area for the given diagram.

First find the area to the left of $-1.28$ and $1.28$. Standard normal table shows that these latter two areas are $0.1003$ and $0.8997$, respectively. The area under the standard normal curve that lies to the right of $1.28$ is, $1-0.8997=0.1003$. Therefore, the area under the standard normal curve that lies to the left of $-1.28$ or to the right of $1.28$ is, $0.1003+0.1003=0.2006$.

Part d Step 1 . Given information

Part d Step 2 . Let us find the area for the given diagram.

First find the area to the left of $-1.64$ and $1.64$. Standard normal table shows that these latter two areas are $0.9495$ and $0.0505$, respectively. The area under the standard normal curve that lies to the right of $1.64$ is, $1-0.9495=0.0505$. The area under the standard normal curve that lies to the left of $-1.64$ or to the right of $1.64$ is, $0.0505+0.0505=0.1010$.