Question

please answer following probability question using CLT(remember to apply continuous correction)

(1) With n=20 births and p=0.512 for a boy, find P(fewer than 8 boys)

(2) With n=20 births and p=0.512 for a boy, find P(no larger than 8 boys)

(3) With n=20 guesses and p=0.2 for a correct answer, find P(at least 6 correct answers)

(4) With n=20 guesses and p=0.2 for a correct answer, find P(more than 6 correct answers)

Answer 1

Ans:

1)

n=20 and p=0.512

mean=20*0.512=10.24

standard deviation=sqrt(20*0.0512*(1-0.0512))=2.235

z=(7.5-10.24)/2.235=-1.226

P(z<=-1.226)=0.1101

2)

z=(8.5-10.24)/2.235=-0.779

P(z<=-0.779)=0.2181

3)n=20 and p=0.2

mean=20*0.2=4

standard deviation=sqrt(20*0.2*0.8)=1.789

z=(5.5-4)/1.789=0.839

P(z>=0.839)=0.2009

4)

P(x>6)=1-P(x<=6)

z=(6.5-4)/1.789

z=1.397

P(x>6)=1-P(z<=1.397)=0.0812