Answer to Question #329324 in Statistics and Probability for Joeff

Question

Identify the region/area under the normal curve corresponding to each of the following.

1.Between Z=0 and z=1.36

2.between z=0 and z=1.87

3.between z=1.36 and z= 2.5

4.between -1.36 and z= -1.87

5. Between z=-1.36 and z=2.5

6.between z=1.36 and z=-2.5

Answer 1

We find from z-table:

$1. \ P(0<Z<1.36) =P(Z<1.36)-P(Z<0)=\\ =0.9131-0.5=0.4131;$

$2. \ P(0<Z<1.87) =P(Z<1.87)-P(Z<0)=\\ =0.9693-0.5=0.4693;$

$3. \ P(1.36<Z<2.5) =\\ =P(Z<2.5)-P(Z<1.36)=\\ =0.9938-0.9131=0.0807;$

$4. \ P(-1.87<Z<-1.36) =\\ =P(Z<-1.36)-P(Z<-1.87)=\\ =0.0869-0.0307=0.0562;$

$5. \ P(-1.36<Z<2.5) =\\ =P(Z<2.5)-P(Z<-1.36)=\\ =0.9938-0.0869=0.9069;$

$6. \ P(-2.5<Z<1.36) =\\ =P(Z<1.36)-P(Z<-2.5)=\\ =0.9131-0.0062=0.9069.$