PLEASE HELP ME WITH THIS

Question

According to a 2009 Reader's Digest article, people throw away about 13% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 194 grocery shoppers to investigate their behavior. What is the probability that the sample proportion does not exceed 8%?

Answer 1

phat is sample proportion

p is population proportion = 0.13

n = sample size = 194

Want to know P(phat < 0.08)

compute z-stat for proportion: z = (phat - p)/sqrt(p * (1-p)/n)

so P(phat < 0.08) = P(z < (0.08 - 0.13)/sqrt(0.08*0.92/194)) = P(z < -2.57) = 0.0051