Question

use the accompanying table of z - scores and percentiles to find the percentage of data items in a normal distribution that lie a. below and b. above a z - score of - 0.25
click the icon to view the table of z - scores and percentiles.
a. the percentage of data items that lie below the z - score is
(round to two decimal places as needed.)

Explanation:

To solve this, we need the z - score (it seems the z - score is - 0.25 from the partial text). We use the standard normal distribution table (z - table) to find the area to the left of the z - score, which represents the percentage of data items below that z - score.

Step 1: Recall the z - table

A z - table gives the cumulative probability $P(Z\leq z)$ for a standard normal random variable $Z$. For a z - score of $z=- 0.25$, we look at the row corresponding to - 0.2 and the column corresponding to 0.05 in the z - table.

Step 2: Find the value from the z - table

Looking up $z = - 0.25$ in the standard normal table, we find that $P(Z\leq - 0.25)=0.4013$.

Step 3: Convert to percentage

To convert this probability to a percentage, we multiply by 100. So, $0.4013\times100 = 40.13\%$

Answer:

40.13%