Question

7.2.5 In 1991, about 105 for every 1,000 Hispanic women between the ages of 15 and 19 gave birth. However, in 2010, only about 56 for every 1,000 Hispanic women between the ages of 15 and 19 gave birth. Source: Statista.

a. If 200 Hispanic women between the ages of 15 and 19 in 1991 were randomly selected, what is the probability that more than 11% of them gave birth?
b. If 200 Hispanic women between the ages of 15 and 19 in 2010 were randomly selected, what is the probability that more than 11% of them gave birth?

Answer 1

a)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.1050
sample size       =n=	200
std error of proportion=σp=√(p*(1-p)/n)=	0.0217

probability =P(X>0.11)=P(Z>(0.11-0.105)/0.022)=P(Z>0.23)=1-P(Z<0.23)=1-0.591=0.4090

b)

here population proportion=     p=	0.056
sample size       =n=	200
std error of proportion=σp=√(p*(1-p)/n)=	0.0163

probability =P(X>0.11)=P(Z>(0.11-0.056)/0.016)=P(Z>3.32)=1-P(Z<3.32)=1-0.9995=0.0005