Q. 6.62 - Elementary Statistics

Question

Use Table to obtain the areas under the standard normal curve. 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. $2.02$.

b. $-0.56$.

c. $-4$.

Step-by-Step Solution

Answer

(a) The area under the standard normal that lies to the right of $2.02$ is $0.0217$

(b) Thus, the area under the standard normal that lies to the right of $-0.56$ is $0.7123$

(c) Thus, the area under the standard normal that lies to the right of $-4$ is $1.0000$

Part(a) Step 1: Given Information

Part(a) Step 2: Explanation

The given number $2.02$ is positive. Therefore, the conventional normal table of positive $z$ scores is applied. To begin, reduce the number in the left hand column labeled '$z$' to $2.0$ and then move across the row to the column labeled '$0.02$ '. The result is $0.9783.$

As a result, the area to the right of $2.02$ under the usual normal is $1-0.9783=0.0217.$

Part(b) Step 1: Given Information

Part(b) Step 2: Explanation

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

The given quantity  is negative, the conventional normal table of negative $z$ scores is applied. First, move down to$-0.5$ in the right-hand column labelled' $z$ ', then across the row to the column labelled' $0.06$ ', and you'll get $0.2877.$

Part(c) Step 1: Given Information

Part(c) Step 2: Explanation

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

Because the given number $-4$ is negative, the conventional normal table of negative $z$ scores is applied. To begin, travel down the right hand column labeled '$z$' to $-4.0$ and then across the row to the column labeled '$0.00$' to obtain the number $0.0000.$