According to a survey in a country 24 of adults do not have

According to a survey in a country, 24% of adults do not have any credit cards. Suppose a simple random sample of 300 adults is obtained. In a random sample of 300 adults, what is the probability that less than 22% have no credit cards?

Solution

So the probability that less than 22% have no credit cards is

P(phat<0.22) = P((phat-p)/sqrt(p*(1-p)/n) <(0.22-0.24)/sqrt(0.24*(1-0.24)/300))

=P(Z<-0.81) = 0.2090 (from standard normal table)