Sample proportion exceeds

Question

According to a 2009 Reader's Digest article, people throw away approximately 11% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 182 grocery shoppers to investigate their behavior. What is the probability that the sample proportion exceeds 0.1?

Answer 1

phat = sample proportion

p = population proportion

n = sample size

transform to z-statistic

z = (phat - p)/sqrt(p*(1-p)/n)

p(phat > 0.1) = p(z > (0.1 - 0.11)/(sqrt(0.11*0.89/182)) = p(z > -0.43) = 1 - p(z < -0.43) = 1 - 0.3336 = 0.6664