Q. 6.61 - Elementary Statistics

Question

Use Table II to obtain the areas under the standard normal curve required in Exercises 6.59-6.66. Sketch a standard normal curve and shade the area of interest in each problem.

Find the area under the standard normal curve that lies to the right of

a. $-1.07$

b. $0.6$

c. $0$

d. $4.2$

Step-by-Step Solution

Answer

a. The area under the standard normal curve that lies to the right of $-1.07$ is $0.8577$

b. The area under the standard normal curve that lies to the right of $0.6$ is $0.2743$

c. The area under the standard normal curve that lies to the right of $0$ is $0.5000$

d. The area under the standard normal curve that lies to the right of $4.2$ is $0.0000$

Part (a) Step 1: Given Information

Under the standard normal, calculate the area lying to the right of $-1.07$

Part (a) Step 2: Explanation

Right-hand area = $1-$Left-hand area

Because the given number $-1.07$ is negative, the conventional normal table of negative $z$ scores is applied.

First, go down to $-1.0$ in the right-hand column labeled $\text{'}z,\text{'}$ and then across the row to the right.

As a result, the area to the right of $-1.07$under the standard normal is $1-0.1423=0.8577.$

Part (b) Step 3: Given Information

Under the standard normal, calculate the area lying to the right of $0.6$

Part (b) Step 4: Explanation

Right-hand area $=1-$ Left-hand area

Because the given quantity $0.6$is positive, the typical normal table of positive $z$ scores is employed. First, move down to $0.6$ in the left hand column labeled $z$ and then across the row to the column labeled $0.00$to get $0.7257.$

As a result, the area beneath the standard normal to the right of $0.6$ is $1-0.7257=0.2743$

Part (c) Step 5: Given Information

Under the standard normal, calculate the area lying to the right of $0$.

Part (c) Step 6: Explanation

Right-hand area $=1-$Left-hand area

The typical table is employed. To begin, move down the left hand column labeled' $\text{'}z\text{'}$ to $0.0$ and then across the row to the column labeled $\text{'}0.00\text{'}$ to get $0.5000$.

As a result, the area beneath the standard normal to the right of $0$ is $1-0.5000=0.5000$.

Part (d) Step 7: Given Information

Under the standard normal, calculate the area lying to the right of $4.2$.

Part (d) Step 8: Explanation

Right-hand area $=1-$Left-hand area

The typical table is employed. To begin, move down the left hand column labeled' $z$' to $4.0$ and then across the row to the column labeled' $0.02$ to get $1.0000$.

As a result, the area beneath the standard normal to the right of $0.42$ is $1-1.0000=0.0000.$