Question

Based on the U.S. Census Bureau’s American Community Survey of 2017, 12.9% of the U.S. population was foreign-born. The U.S. Census Bureau uses the term foreign-born to refer to anyone who is not a U.S. citizen at birth. When I took a sample of 5 students from my statistics class find the following probabilities:

1 Find the probability that none of the students are foreign-born (x=0)
2 find p(x>=1) (that at least one is foreign-born)

Answer 1

0.52474, 0.47526

Explanation:

given that based in the U.S. Census Bureau’s American Community Survey of 2017, 12.9% of the U.S. population was foreign-born.

The U.S. Census Bureau uses the term foreign-born to refer to anyone who is not a U.S. citizen at birth.

Hence for a randomly selected citizen to be foreign born has constant probability 12.9% since each person is independent of the other and there are only two outcomes.

For the sample of 5 students, X = foreign born is binomial (5, 0.129)

1) the probability that none of the students are foreign-born (x=0)

=
`(1-0.129)^5\\= 0.52474`

2 p(x>=1) (that at least one is foreign-born)

=
`1-P(0)\\=1-0.52474\\= 0.47526`