Question

According to a regional Bar​ Association, approximately 64​% of the people who take the bar exam to practice law in the region pass the exam. Find the approximate probability that at least 67​% of 400 randomly sampled people taking the bar exam will pass. Answer the questions below. The sample proportion is 0.67. What is the population​ proportion?

Answer 1

What is the population​ proportion =0.64

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.640
sample size       =n=	400
std error of proportion=σp=√(p*(1-p)/n)=	0.0240

approximate probability that at least 67​% of 400 randomly sampled people taking the bar exam will pass :

probability =P(X>0.67)=P(Z>(0.67-0.64)/0.024)=P(Z>1.25)=1-P(Z<1.25)=1-0.8944=0.1056