Question

Consider the following. (Give your answers correct to four decimal places.)

(a) Find P(-2 < z < 0.00).

(b) Find P(-1.87 < z < 2.07).

(c) Find P(z < -1.44).

(d) Find P(z < -0.45).

(e) Find P(-3.1 < z < 0.00).

(f) Find P(-2.41 < z < 1.34).

(g) Find P(z < -2.23).

(h) Find P(z > 2.34).

Answer 1

(a) P(-2<Z<0.00)=P(Z>-2)-P(Z>0)

=1-P(Z<-2)-P(Z>0)

=1-P(Z>2)-P(Z>0) , Due to symmetry

=1-0.022750-0.5

=0.4773

(b) P(-1.87<Z<2.07)=P(Z>-1.87)-P(Z>2.07)

=1-P(Z<-1.87)-P(Z>2.07)

=1-P(Z>1.87)-P(Z>2.07) ; Due to symmetry

=1-0.030742-0.019226

=0.9500

(c) P(Z<-1.44)=P(Z>1.44) Due to symmetry

=0.0749

(d)P(Z<-0.45)=P(Z>0.45) ; Due to symmetry

=0.3264

(e) P(-3.1<Z<0)=P(Z>-3.1)-P(Z>0)

=1-P(Z<-3.1)-P(Z>0)

=1-P(Z>3.1)-P(Z>0) ; Due to symmetry

=1-0.00096760-0.5

=0.4990

(f) P(-2.41<Z<1.34)=P(Z>-2.41)-P(Z>1.34)

=1-P(Z<-2.41)-P(Z>1.34)

=1-P(Z>2.41)-P(Z>1.34)

=1-0.0081975-0.090123

=0.9017

(g) P(Z<-2.23)=P(Z>2.23) ; Due to symmetry

=0.0129

(h) P(Z>2.34)=0.0964