Question

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

Short answer

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

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,$0.1010$.

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 $-1.96$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,role="math" localid="1652687589152" $0.9901-0.0099=0.9802$.

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,$0.0505+0.0505=0.1010$.