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? Why?
A hypergeometric distribution, as the probability of being chosen on a trial is dependent on the outcome of previous trials.
A hypergeometric distribution, as the probability of being chosen on a trial is independent of the outcomes of previous trials.
A binomial distribution, as the probability of being chosen on a trial is dependent of the outcomes of previous trials.
A binomial distribution, as the probability of being chosen on a trial is either a success or a failure.
(b) Find the probability that four or more internship trained candidates are hired. (Round your answer to four decimal places.)
0.4459
(c) What is the mean and standard deviation of Y? (Round your answers to four decimal places.)
$\mu = 2.7273$
$\sigma = 0.8628$
