Studies have shown that 24 of all students at Richardson Hig

Studies have shown that 24% of all students at Richardson High School smoke. Suppose we happen to observe a random sample of 70 Richardson High School students in the school cafeteria. What is the probability that the proportion of those 70 students in the cafeteria who smoke is no more than 20%.

Solution

So the probability that the proportion of those 70 students in the cafeteria who smoke is no more than 20% is

P(phat<0.2)

= P((phat-p)/sqrt(p*(1-p)/n) <(0.2-0.24)/sqrt(0.24*(1-0.24)/70))

=P(Z<-0.78) = 0.2177 (from standard normal table)