Question

The Census Bureau's Current Population Survey shows that 28% of individuals, ages 25 and older, have completed four years of college. For a sample of 15 individuals, ages 25 and older, what is the probability that five will have completed four years of college?

Answer 1

19.35% probability that five will have completed four years of college

Explanation:

For each individual chosen, there are only two possible outcomes. Either they have completed fourr years of college, or they have not. The probability of an adult completing four years of college is independent of any other adult. So the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

28% of individuals

This means that
`p = 0.25`

For a sample of 15 individuals, ages 25 and older, what is the probability that five will have completed four years of college?

This is P(X = 5) when n = 15. So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 5) = C_(15,5).(0.28)^(5).(0.72)^(10) = 0.1935`

19.35% probability that five will have completed four years of college