Q. 6.68 - Elementary Statistics

Question

6.68 Use Table II to obtain each shaded area under the standard normal curve.

Step-by-Step Solution

Answer

a. $0.9500$

b. $0.9802$

c. $0.2006$

d. $0.1010$

Part (a) Step 1: Given Information

The given graph is:

Part (a) Step 2: Explanation

Subtracting the smaller area from the bigger area yields the area under the normal curve between two specified $z-$scores.

There is an area between two $z-$scores equal to the larger of the two supplied areas minus the smaller of the two given areas.

Thus, the area under the standard normal curve to the left of $1.96$ is $0.9750$, whereas the area under the standard normal curve to the left of $-1.96$ is $0.0250$.

As a result, the area between $-1.96$ and $1.96$ under the usual normal will be $0.9750-0.0250=0.9500.$

So, the shaded area is $0.9500$

Part (b) Step 3: Given Information

The given graph is:

Part (a) Step 2: Explanation

Subtracting the smaller area from the bigger area yields the area under the normal curve between two specified $z-$scores.

There is an area between two $z-$scores equal to the larger of the two supplied areas minus the smaller of the two given areas.

Thus, the area under the standard normal curve to the left of $2.33$ is $0.9901$, whereas the area under the standard normal curve to the left of $-2.33$ is $0.0099$

As a result, the area between $-2.33$ and $2.33$ under the usual normal will be $0.9901-0.0099=0.9802$

So, the shaded area is $0.9802$

Part (c) Step 5: Given Information

The given graph is:

Part (c) Step 6: Explanation

To the left of $-1.28$, the area under the standard normal curve is $0.1003.$

$Area to the right =1- Area to the left$

To the left of $1.28,$ the area under the standard normal curve is $0.1003.$

$1-0.8997=0.1003$ is the area to the right of $1.28.$

As a result, the area beneath the standard normal to the left of $-1.28$ and to the right of $1.28$will be $0.1003+0.1003=0.2006.$

Part (d) Step 7: Given Information

The given graph is:

Part (d) Step 8: Explanation

To the left of $-1.64$, the area under the standard normal curve is $0.0505$

$Area to the right =1- Area to the left$

To the left of $-1.64$, the area under the standard normal curve is $0.9495$$0.9495$.

$1-0.9495=0.0505$  is the area to the right of $1.64$

As a result, the area beneath the standard normal to the left of $-1.64$ and to the right of $1.64$ will be $0.0505+0.0505=0.1010.$