Question

Suppose 52% of the population has a college degree. If a random sample of size 563 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by more than 5%? Round your answer to four decimal places.

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.520
sample size       =n=	563
std error of proportion=σp=√(p*(1-p)/n)=	0.0211

proportion of persons with a college degree will differ from the population proportion by more than 5%

=P(P>0.57)+P(P<0.47)=1-P(0.47<X<0.57)=1-P(-0.05/0.0211<Z<0.05/0.0211)=1-P(-2.37<Z<2.37)=1-(0.9912-0.0088)

=0.0176 (please try 0.0178 if this comes wrong due to rounding error and revert)