Question

Although studies continue to show smoking leads to significant health problems, 20% of adults in the United States smoke. Consider a group of 200 adults.

If required, round your answers to four decimal places. Use Table 1 in Appendix B. If your answer is zero, enter "0".

a. What is the expected number of adults who smoke?

b. What is the probability that fewer than 40 smoke? Used continuity correction factor.

c. What is the probability that from 35 to 60 smoke? Used continuity correction factor.

d. What is the probability that 90 or more smoke? Used continuity correction factor.

Answer 1

Ans:

Normal approximation:

mean=200*0.2=40

standard deviation=sqrt(200*0.2*(1-0.2))=5.657

a)expected number of adults who smoke=200*0.2=40

b)

P(x<40)=P(x<=39)

z=(39.5-40)/5.657=-0.088

P(z<=-0.088)=0.4648

c)

P(35<=x<=60)=P(x<=60)-P(x<=34)

z(60.5)=(60.5-40)/5.657=3.624

z(34)=(34.5-40)/5.657=-0.972

P(-0.972<z<3.624)=P(z<3.624)-P(z<-0.972)

=0.9999-0.1655=0.8344

d)

P(x>=90)=1-P(x<=89)

z=(89.5-40)/5.657=8.75

P(x>=90)=1-P(x<=8.75)

=1-1=0.0000