College students often make up a substantial portion of the population of college cities and towns. State College, Pennsylvania, ranks first with 71.1% of its population made up of college students. What is the probability that in a random sample of 150 people from State College, more than 50 are not college students? Solution Given p=1-0.711=0.289 By using Normal approximation, X~Normal(mean=n*p=150*0.289=43.35, s=n*p*(1-p)=sqrt(150*0.289*0.711)=5.55) The probability is P(X>50)=P((X-mean)/s >(50-43.35)/5.55) =P(Z> 1.2) =0.1151 (check standard normal table).

1. College students often make up a substantial portion of the population of college cities and
towns. State College, Pennsylvania, ranks first with 71.1% of its population made up of college
students. What is the probability that in a random sample of 150 people from State College, more
than 50 are not college students?
Solution
Given p=1-0.711=0.289
By using Normal approximation,
X~Normal(mean=n*p=150*0.289=43.35, s=n*p*(1-p)=sqrt(150*0.289*0.711)=5.55)
The probability is
P(X>50)=P((X-mean)/s >(50-43.35)/5.55)
=P(Z> 1.2)
=0.1151 (check standard normal table)