Answer
to fined Z score ,
at
$x=108$ -->$z=0.4 $
$x=115$ -->$z= 0.75 $
$x=130$ -->$z= 1.5 $
$x=90$ -->$z=-0.5 $
$x=88$ -->$z= -0.6 $
$x=95$ -->$z= -0.25 $
to fined X value
at
$z=-0.40$ -->$x=92$
$z=-0.50$ -->$x=90$
$z=1.8$ -->$x=136$
$z=-0.75$ -->$x=115$
$z=1.5$ -->$x=130$
$z=-1.25$ -->$x=75$
Work Step by Step
to fined Z score , we use
$$
z=\frac{X-\mu}{\sigma}
$$
then at
$x=108$ -->$z= \frac{108-100}{20} =0.4 $
$x=115$ -->$z= \frac{115-100}{20} =0.75 $
$x=130$ -->$z= \frac{130-100}{20} =1.5 $
$x=90$ -->$z= \frac{90-100}{20} =-0.5 $
$x=88$ -->$z= \frac{88-100}{20} =-0.6 $
$x=95$ -->$z= \frac{95-100}{20} =-0.25 $
to fined X value , we use
$$
X=Z \sigma+ \mu
$$
then at
$z=-0.40$ -->$x=-0.40*20 +100 =92$
$z=-0.50$ -->$x=-0.50*20 +100 =90$
$z=1.8$ -->$x=1.8*20 +100 =136$
$z=-0.75$ -->$x=0.75*20 +100 =115$
$z=1.5$ -->$x=1.5*20 +100 =130$
$z=-1.25$ -->$x=-1.25*20 +100 =75$
