Question

An SRS of 1000 students are asked, "Do you think cell phones make people happier?" If in fact 30% of the population of students believe that cell phones do indeed increase happiness, then what are the chances that at most 31% of the people in the sample will answer "yes"?

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.300
sample size       =n=	1000
std error of proportion=σp=√(p*(1-p)/n)=	0.0145

chances that at most 31% of the people in the sample will answer "yes":

probability =P(X<0.31)=(Z<(0.31-0.3)/0.014)=P(Z<0.69)=0.7549