Q. 6.67 - 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, $0.7994$.

Part$\left(b\right)$: The required area is, $0.8990$.

Part$\left(c\right)$: The required area is, $0.0500$.

Part$\left(d\right)$: The required area is,$0.0198$.

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 $-1.28$ and $1.28$ equals the area to the left of $1.28$ minus the area to the left of $-1.28$. Standard normal table shows that these latter two areas are $0.8997$ and $0.1003$ respectively. So, the required area is, $0.8997-0.1003=0.7994$.

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 $-1.64$ and $1.64$ equals the area to the left of $1.64$ minus the area to the left of $-1.64$. Standard normal table shows that these latter two areas are $0.9495$ and $0.0505$, respectively. So, the required area is, $0.9495-0.0505=0.8990$.

Part c Step 1 . Given information

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

First we need to find the area to the left of $-1.96$ and $1.96$. Standard normal table shows that these latter two areas are $0.0250$ and $0.9750$, respectively. The area under the standard normal curve that lies to the right of $1.96$ is, $1-0.9750=0.0250$. Therefore, the area under the standard normal curve that lies to the left of $-1.96$ or to the right of $1.96$ is, $0.0250+0.0250=0.0500$.

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 $-2.33$ and $2.33$. Standard normal table shows that these latter two areas are $0.0099$ and $0.9901$,respectively. The area under the standard normal curve that lies to the right of $2.33$ is, $1-0.9901=0.0099$. Therefore, the area under the standard normal curve that lies to the left of $-2.33$ or to the right of $2.33$ is, $0.0099+0.0099=0.0198$.