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 - 2.5. 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 0.62 %. (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: Recall total percentage in normal - distribution

The total percentage of data in a normal distribution is 100%.

Step2: Calculate percentage above z - score

We know the percentage of data items below a z - score of - 2.5 is 0.62%. To find the percentage of data items above the z - score, we subtract the percentage below from 100%. Let \(P_{above}\) be the percentage above the z - score and \(P_{below}\) be the percentage below the z - score. Then \(P_{above}=100 - P_{below}\).
\[P_{above}=100 - 0.62=99.38\]

Answer:

99.38