6.00 point Exercise 6.40 METHODS AND APPLICATIONS Suppose thai x has a bnomial d

Question

6.00 point Exercise 6.40 METHODS AND APPLICATIONS Suppose thai x has a bnomial distribution wrth n 200 and p 0 43 IRound np and n(1-Dl answers to 2 decimal places, Round your answers to 4 decimal places Round z values to 2 decimal places Round tre intermediate value [cj to 4 decimal places.) a) Show that the notmal approx manion to the binomial can appropr alely be used to cakcuiate probabities about x iby Make cominuny comections tor esch of the folowng and then use the nomal appiooumatian to the bnomiarto ting eacn probscity caS Book &Resources;

Explanation / Answer

We have given that,

n=200,p=0.43.

Xbin(n,p)

Mean=u=np=200*0.43

=86.

Var(x)=sig=np(1-P)

=86*(1-0.43)

=86*0.57

=49.04

b)

P(x=80)=P((x-u))/sig)=(80-86)/49.04)

=p(Z=-0.12)

=0.4522.

P(x<97)=P(((x-u)/sig)<(97-86)/49.04)

=P(z<0.22)

=0.5871. (Z table value)

Same procedure,p(x<74)=P(z<(74-86)/49.04)

=P(z<-0.25)

=0.4013.

P(x>103)=1-P(x<103)

=1-P(z<(103-86)/49.04)

=1-P(z<0.35)

=1-0.6368

=0.3632.

P(x>104)=1-P(z<0.37)

=1-0.6443

=0.3557.

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