Q. 6.66

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 $- 1$ or to the right of $2$ .

b. either to the left of $- 2.51$ or to the right of $- 1$ .

Step-by-Step Solution

Verified

Answer

(a) The area under the standard normal that lies either to the left of $- 1$ or to the right of $2$ will be $0.1815$

(b) The area under the standard normal that lies either to the left of $- 2.51$ or to the right of $- 1$ is

$0.8473$

1Part(a) Step 1: Given Information

2Part(a) Step 2: Explanation

To the left of $- 1$ is the following area:

Because the given integer $- 1$ is negative, the conventional normal table of negative $z$ scores is applied. To begin, move down the right hand column labeled' $z$ 'to $- 1.0$ and then across the row to the column labeled' $0.00$ 'to get $0.1587$ .

Right-hand side of $2$ :

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

Because the given number 2 is positive, the typical normal table of positive $z$ scores is applied. To begin, move down the left hand column labeled' $z$ 'to $2.0$ and then across the row to the column labeled' $0.00$ 'to get $0.9772$

Consequently the area under the standard normal that lies to the right of $2.0$ is $1 - 0.9772 = 0.0228$

The area is $0.1587 + 0.0228 = 0.1815$ .

3Part(b) Step 1: Given Information

4Part(b) Step 2: Explanation

Because the given integer $- 2.51$ is negative, the typical normal table of negative $z$ scores is utilised in the area to the left of $- 2.51$ . To begin, move down the right hand column labelled $z$ 'to $- 2.5$ and then across the row to the column labeled' $0.01$ 'to get $0.0060$ .