Answer to Question #207777 in Statistics and Probability for pesky

Question

find the value of Z such that

i. the area of the right of Z is 0.2266

ii. the area between -Z and Z is 0.5722

Answer 1

Solution:

(i) $P(Z>z)=0.2266$

$P(Z\le z)=1-P(Z>z)=1-0.2266=0.7734$

From z-score table:

$z=0.75$

(ii) $P(-z<Z<z)=0.5722$

$P(Z< z)-P(Z<-z)=P(Z<z)-[1-P(Z<z)] \\=2P(Z<z)-1=0.5722$

$\Rightarrow 2P(Z<z)=1.5722 \\ \Rightarrow P(Z<z)=0.7861$

From z-score table:

$z=0.795$