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 being made up of college students. Let 150 people from State College, PA be randomly selected. Find the probability that in a random sample of 150 State College residents, more than 50 are college students. (Verify that the normal distribution can be used to approximate the binomial distribution in this problem). Solution mean=150*0.711=106.65 s=sqrt(150*0.711*(1-0.711))=5.551743 So the probability is P(X>50) = P((X-mean)/s >(50-106.65)/5.551743) =P(Z>-10.204) =1 (from 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 being made up of
college students. Let 150 people from State College, PA be randomly selected. Find the
probability that in a random sample of 150 State College residents, more than 50 are college
students. (Verify that the normal distribution can be used to approximate the binomial
distribution in this problem).
Solution
mean=150*0.711=106.65
s=sqrt(150*0.711*(1-0.711))=5.551743
So the probability is
P(X>50) = P((X-mean)/s >(50-106.65)/5.551743)
=P(Z>-10.204) =1 (from standard normal table)