Question

use the accompanying table of z - scores and percentiles to find the percentage of data terms in a normal distribution that lie between ( z = 0.5 ) and ( z = 2.6 ).
click the icon to view the table of z - scores and percentiles.
the percentage of data terms in a normal distribution that lie between ( z = 0.5 ) and ( z = 2.6 ) is (square%)
(round to two decimal places as needed.)

Explanation:

Step1: Find 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 percentile for \(z = 2.6\)

From the z - score table, the percentile for \(z = 2.6\) is \(99.53\%\) (this means \(99.53\%\) of the data lies to the left of \(z=2.6\)).

Step3: Calculate the percentage between \(z = 0.5\) and \(z=2.6\)

We use the formula \(P(0.5<Z<2.6)=P(Z < 2.6)-P(Z < 0.5)\)
Substitute the values: \(99.53\% - 69.15\%=30.38\%\)

Answer:

\(30.38\)