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 - 0.20. 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 ) b. the percentage of data items that lie above the z - score is □%. (round to two decimal places as needed )

Explanation:

Step1: Find the percentile for \(z = - 0.20\)

Looking up the \(z\)-score of \(-0.20\) in the standard \(z\)-score and percentile table. The percentile corresponding to \(z=-0.20\) is \(42.07\%\). This percentile represents the percentage of data items below the \(z\)-score.

Step2: Calculate the percentage above the \(z\)-score

Since the total percentage of data in a distribution is \(100\%\), to find the percentage of data items above the \(z\)-score, we use the formula \(100\%-\text{percentage below the }z-\text{score}\). So, \(100\% - 42.07\%=57.93\%\)

Answer:

a. \(42.07\%\)
b. \(57.93\%\)