Question

Use Cumulative Standardized Normal Probability table to find the area under the standard normal curve between the following values:

a) z=0 and z=2.3

b) z=0 and z=1.68

c) z=0.24 and z=0.33

d) z=-2.75 and z=0

e) z=-2.81 and z=-1.35

f) z=-1.73 and z=0.49

Answer 1

a) z=0 and z=2.3

$P(0<z<2.3)=0.4893$

b) z=0 and z=1.68

$P(0<z<1.68)=0.4535$

c) z=0.24 and z=0.33

$P(0.24<z<0.33)=P(0<z<0.33)-P(0<z<0.24)$

$=0.1293-0.0948\\=0.0345$

d) z=-2.75 and z=0

$P(-2.75<z<0)=P(0<z<2.75)=0.4970$

e) z=-2.81 and z=-1.35

$P(-2.81<z<-1.35)=P(1.35<z<2.81)$

$=P(0<z<2.81)-P(0<z<1.35)\\=0.4975-0.4115\\=0.086$

f) z=-1.73 and z=0.49

$P(-1.73<z<0.49)=P(0<z<1.73)+P(0<z<0.49)$

$=0.4582+0.1879\\=0.6451$