Question

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 134 of people from State College, more than 50 are not college students? Round the final answer to at least decimal places and intermediate -value calculations to decimal places.

Answer 1

Proportion of college students in the state = 71.1% = 0.711

Therefore proportion of people who are not college students = 1 - 0.711 = 0.289

Let X= Selected person is not college student.

n = 134  

X follows binomial distribution with probability p = 0.289 and n = 134.

We use normal approximation since n is very large. Parameters of normal distributions are:

= np = 134 * 0.289 = 38.726  

[Note that in the provided question, to what decimal places I have to round answer is not visible. So I round up intermediate -value to 3 decimal places and final answer to 4 decimal places]

= npq = 134 * 0.289 * 0.711 = 27.534

We want P(X>50), by using continuity correction,

P(X>50) = P(X > 50.5)

1 - 0.9875

0.0125

Hence probability that  more than 50 selected people are not college students is 0.0125