Question

A political committee consists of 8 Democrats and seven republicans. A subcommittee of nine people needs to be formed for this group. (For this problem, define a success as a democrat being selected for the subcommittee.)

A. Determine the probability that this subcommittee will consist of seven Democrats and two republicans if they were randomly selected.

B. Calculate the mean and standard deviation of this distribution.

Answer 1

solution=

a) A political committee consists of 8 Democrats and 7 republicans

Total Democrats = 8
Total Republicans = 7
Total Democrats + Republicans = 15

probability of selecting seven democrats = 8C7
probability of selecting two republicans = 7C2
Total # of people selected = 9

= (8C7)(7C2) / 15C9
= (8)(21) / 5005 = 0.0336=3.36%(answer)

b)here
n= total people = 15
p= proportion of select people in committee
p = 1/15 =0.067
if follows binomial distribution
mean = np= 15*0.067 =1.005
standard deviaion=sqrt n*p*(1-p)
sqrt 15(0.067)(1-0.067)= 0.9683