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 - 0.70.
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 \(z = - 0.70\)

Looking up the \(z\)-score of \(-0.70\) in the standard normal distribution table (table of \(z\)-scores and percentiles). The percentile corresponding to \(z=-0.70\) is \(24.20\%\). 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 normal distribution is \(100\%\), to find the percentage of data items above the \(z\)-score, we use the formula \(100\%-\text{percentage below}\). So, \(100 - 24.20=75.80\%\)

Answer:

a. \(24.20\)
b. \(75.80\)