Q. 6.65 - 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

a. either to the left of $-2.12$ or to the right of $1.67$.

b. either to the left of $0.63$ or to the right of $1.54$.

Step-by-Step Solution

Answer

(a) The area under the standard normal that lies either to the left of $-2.12$ or to the right of $1.67$ will be $0.0645$

(b) The area under the standard normal that lies either to the left of $0.63$ or to the right of $1.54$ will be  $0.7975$

Part(a) Step 1: Given Information

Part(a) Step 2: Explanation

$-2.12$ area to the left:

Because the given number $-2.12$ is negative, the conventional normal table of negative $z$ scores is applied. To begin, move down the right hand column labeled' $z$ 'to $-2.1$ and then across the row to the column labelled'$0.02$'to get $0.0170$.

$1.67$ area to the right:

Right-hand area $=1$ - Left-hand area

Because the given amount $1.67$ is positive, the conventional normal table of positive $z$ scores is applied. To begin, go down the left hand column labeled' $z$'to $1.6$ and then across the row to the column labeled' $0.07$'to get $0.9525$.

Thus, the area under the standard normal that lies to the right of $1.67$ is $1-0.9525=0.0475$

The area is $0.0170+0.0475=0.0645$

Part(b) Step 1: Given Information

Part(b) Step 2: Explanation

$-2.12$ area to the left:

Because the given value $0.63$ is positive, the typical normal table of positive $z$ scores is employed. To begin, move down the left hand column labeled' $z$ 'to $0.6$ and then across the row to the column labeled' $0.03$'to get $0.7357$.

$1.67$ area to the right:

Right-hand area $=1$ - Left-hand area

Because the given number $1.54$ is positive, the typical normal table of positive $z$ scores is employed. To begin, move down the left hand column labeled' $z$ 'to $1.5$ and then across the row to the column labeled' $0.04$'to get $0.9382$.

Thus, the area under the standard normal that lies to the right of $1.54$ is $1-0.9382=0.0618$

The area is $0.7357+0.0618=0.7975$