Question

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

Short 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,$0.0198$.

Step-by-step solution

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,$0.0099+0.0099=0.0198$.