1) (30 points) Suppose that we have a room with 30 GGC students. In this room, 1
ID: 2930288 • Letter: 1
Question
1) (30 points) Suppose that we have a room with 30 GGC students. In this room, 10 of these students are international students. The college is interested in forming an 8-person committee to explore issues facing todays college students. The 8 students are randomly selected from the group of 30 people in the room? a) What is the probability of equal representation on the committee (4 US students and 4 international students)? b) What is the variance of the number of international students on the com- mittee? c) Suppose that there were equal numbers of each group in the room of 30 people (15 US students and 15 international students), what is the vari- ance for the number of international students on the 8-person committce? d) In non math terms, describe why your answer in part c increased or decreased from part b.Explanation / Answer
Ans:
a)10 international and 20 US students
Probability of equal representation=10C4*20C4/30C8
=210*4845/5852925
=0.1738
b)Probability of a international srudent,p=10/30=1/3=0.33
Probability of US student=20/30=0.67
Let X is number of internation students in committe
Binomial random variable with n=8,p=0.33
Variance=8*0.33*(1-0.33)=1.78
c)Now,n=8,p=15/30=0.5
variance=8*0.5*(1-0.5)=8*0.25=2
d)variance is increased in part b,as now there are more number of students of international group.
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