Question

In southern California, a growing number of individuals pursuing teaching credentials are choosing paid internships over traditional student teaching programs. A group of eleven candidates for five local teaching positions consisted of six who had enrolled in paid internships and five who enrolled in traditional student teaching programs. All eleven candidates appear to be equally qualified, so five are randomly selected to fill the open positions. Let Y be the number of internship trained candidates who are hired. (a) Does Y have a binomial or hypergeometric distribution

Answer 1

Candidates are chosen without replacement, thus trials are dependent, meaning that Y has a hypergeometric distribution.

Explanation:

Difference between hypergeometric and binomial distributions:

In the hypergeometric distribution, trials are dependent of other trials, while in the binomial distribution, they are independent. This can be examplified that in the hypergeometric distribution, the candidates are chosen from a set without replacement, while in the binomial distribution they are chosen with replacement.

In this question:

Candidates are chosen without replacement, thus trials are dependent, meaning that Y has a hypergeometric distribution.