Answer to Question #122000 in Statistics and Probability for Yoggaranee

Question

Four of the Statistics for Business and Economics students submitted an entry to a Math contest at the faculty. A total of 24 entries were submitted. Six of the entries will move on to the next round.

a. What is the hypergeometric probability that all four Statistics for Business and Economics students will move on to the next round? (2 Marks)
b. How many Statistics for Business and Economics students are expected to move to the next round?
(2 Marks)
c. What is the hypergeometric probability that fewer Statistics for Business and Economics students than expected will make it to the next round?

Answer 1

$(a) P(x=4)= (\begin{pmatrix} 6 \\ 4 \end{pmatrix} * \begin{pmatrix} 18 \\ 0 \end{pmatrix})/ \begin{pmatrix} 24 \\ 4 \end{pmatrix} =0.0014$

$(b) E(x)=n*(s/N)=4*(6/24)=1$

$(c) P(x=0)= (\begin{pmatrix} 6 \\ 0 \end{pmatrix} * \begin{pmatrix} 24-6 \\ 4 \end{pmatrix})/ \begin{pmatrix} 24 \\ 4 \end{pmatrix}=0.2880$