Question

Goofy's fast food center wishes to estimate the proportion of people in its city that will purchase its products. Suppose the true proportion is 0.05. If 254 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.03? Round your answer to four decimal places.

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.050
sample size       =n=	254
std error of proportion=σp=√(p*(1-p)/n)=	0.0137

probability that the sample proportion will differ from the population proportion by less than 0.03 :

probability =

P(0.02<X<0.08)

=

P(-2.19<Z<2.19)=

0.9857-0.0143=

0.9714