Q:

Suppose that 60​% of the voters in a state intend to vote for a certain candidate. What is the probability that a survey polling 5 people reveals that at most 2 voters support the candidate.

Accepted Solution

A:
Answer: 0.31744Step-by-step explanation:Binomial probability distribution formula :-[tex]P(X)=^nC_x \ p^x\ (1-p)^{n-x}[/tex], where P(x) is the probability of getting success in x trials, n is total number of trials and p is the probability of getting succes in each trial.Given : The probability that the voters in a state intend to vote for a certain candidate: Β [tex]p=0.60[/tex]Now, the probability that a survey polling 5 people reveals that at most 2 voters support the candidate will be :-[tex]P(x\leq2)=P(0)+P(1)+P(2)\\\\=^5C_0 \ (0.60)^0\ (0.40)^{5}+^5C_1 \ (0.60)^1\ (0.40)^{4}+^5C_2 \ (0.60)^2\ (0.40)^{3}\\\\=(0.40)^5+5(0.60)(0.40)^4+10(0.60)^2(0.40)^3=0.31744[/tex]Hence, the probability that a survey polling 5 people reveals that at most 2 voters support the candidate = 0.31744