Question

use the table below to find the percentage of data items in a normal distribution that lie between ( z=-1.5 ) and ( z=-0.4 ).
click the icon to view the table.
the percentage of data items in a normal distribution that lie between ( z=-1.5 ) and ( z=-0.4 ) is (square %).
(type an integer or a decimal.)

Explanation:

Step1: Find the area to the left of \( z = -0.4 \)

Using the standard normal distribution table (z - table), the area to the left of \( z=-0.4 \) is approximately \( 0.3446 \).

Step2: Find the area to the left of \( z = -1.5 \)

Using the standard normal distribution table, the area to the left of \( z = -1.5 \) is approximately \( 0.0668 \).

Step3: Calculate the area between \( z=-1.5 \) and \( z = -0.4 \)

To find the area between two z - scores, we subtract the smaller area from the larger area. So, the area between \( z=-1.5 \) and \( z=-0.4 \) is \( 0.3446- 0.0668=0.2778 \).

Step4: Convert the area to a percentage

To convert the area (a proportion) to a percentage, we multiply by 100. So, \( 0.2778\times100 = 27.78\% \).

Answer:

\( 27.78 \)