A university must choose a team of 5 students to participate in a TV quiz show. The students will be chosen atrandom from a pool of 44 potential participants of whom 20 are women. The random variable X represents thenumber of women on the team.
A) hypergeometric; $\mathrm { N } = 44 , \mathrm { n } = 5 , \mathrm { k } = 20 , \mathrm { x } = 0,1,2,3,4,5$
B) hypergeometric; $\mathrm { N } = 44 , \mathrm { n } = 20 , \mathrm { k } = 5 , \mathrm { x } = 0,1,2,3,4,5$
C) hypergeometric; $\mathrm { N } = 44 , \mathrm { n } = 5 , \mathrm { k } = 20 , \mathrm { x } = 0,1,2 , \ldots , 20$
D) not hypergeometric

Question

A university must choose a team of 5 students to participate in a TV quiz show. The students will be chosen atrandom from a pool of 44 potential participants of whom 20 are women. The random variable X represents thenumber of women on the team. 
A) hypergeometric; $\mathrm { N } = 44 , \mathrm { n } = 5 , \mathrm { k } = 20 , \mathrm { x } = 0,1,2,3,4,5$
B) hypergeometric; $\mathrm { N } = 44 , \mathrm { n } = 20 , \mathrm { k } = 5 , \mathrm { x } = 0,1,2,3,4,5$
C) hypergeometric; $\mathrm { N } = 44 , \mathrm { n } = 5 , \mathrm { k } = 20 , \mathrm { x } = 0,1,2 , \ldots , 20$
D) not hypergeometric

Quizplus · Accepted Answer

The situation described is a classic example of a hypergeometric distribution because the team is chosen without replacement from a finite pool of candidates, and the question involves categorizing these candidates into two groups (women and not women). The correct parameters for a hypergeometric distribution in this context are: total population size $N = 44$, number of draws $n = 5$, number of successes in the population $k = 20$ (the number of women), and the number of successes in the sample $x$ can range from 0 to 5 (the number of women selected onto the team).

A University Must Choose a Team of 5 Students to Participate