Question

In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 8% of voters are Independent. A survey asked 29 people to identify themselves as Democrat, Republican, or Independent.

A. What is the probability that none of the people are Independent?

Probability =

B. What is the probability that fewer than 7 are Independent? (HINT: This is easiest in R with the pbinom function)

Probability =

C. What is the probability that more than 2 people are Independent? (HINT: This is easiest in R with the pbinom function)

Probability =

Answer 1

here we use binomial distribution with parameter n=29 and p=0.08 and for

Binomial distribution ,P(X=r)=ⁿC_rp^r(1-p)^n-r  

(A) probability that none of the people are Independent=P(X=0)=0.0891 ( using ms-excel==BINOMDIST(0,29,0.08,0))

(B)probability that fewer than 7 are Independent=P(X<7)=P(X<=6)=0.9932 ( using ms-excel=BINOMDIST(6,29,0.08,1))

(C)probability that more than 2 people are Independent=P(X>2)=1-P(X<=1)=1-0.3138=0.6862

( using ms-excel=BINOMDIST(1,29,0.08,1))