Question

use the accompanying table of z - scores and percentiles to find the percentage of data items in a normal distribution that lie between ( z = 0.5 ) and ( z = 2.9 ). click the icon to view the table of z - scores and percentiles. the percentage of data items in a normal distribution that lie between ( z = 0.5 ) and ( z = 2.9 ) is (square%). (round to two decimal places as needed.)

Explanation:

Step1: Find the percentile for \(z = 0.5\)

From the \(z -\)score table, the percentile for \(z=0.5\) is \(69.15\%\) (this means \(69.15\%\) of the data lies to the left of \(z = 0.5\)).

Step2: Find the percentile for \(z = 2.9\)

From the \(z -\)score table, the percentile for \(z = 2.9\) is \(99.81\%\) (this means \(99.81\%\) of the data lies to the left of \(z=2.9\)).

Step3: Calculate the percentage between \(z = 0.5\) and \(z = 2.9\)

Subtract the smaller percentile from the larger one. Let \(P\) be the percentage of data between \(z = 0.5\) and \(z=2.9\). Then \(P=99.81\% - 69.15\%\)

$$P=(99.81 - 69.15)\%=30.66\%$$

Answer:

\(30.66\)