Question

OM LIS Next Problem Results for this submission Entered Answer Preview 0.1765 Result 0.1765 incorrect 0.9997 0.9997 correct 0.9408 0.9408 0.9408 incorrect At least one of the answers above is NOT correct. (1 point) In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 5% of voters are independent. A survey asked 17 people to identify themselves as Democrat, Republican, or Independent. Find the requested probabilities, to four decimal places. a) What is the probability that none of the people are Independent? 1765 b) What is the probability that fewer than 5 are independent? .9997 c) What is the probability that more than 3 people are independent? 9408 AAD 0 2 823 PM 15/2020 Note: You can eam partial credit on this problem. DEL 9 w Pue e

Answer 1

5% of the voters are independent. This is same as, the probability that a randomly selected voter is independent is 0.05

Let X be the number in a sample of 17 who are independent. We can say that X has a Binomial distribution with parameters, number of trials (number of randomly selected people) n=17 and success probability (the probability that a randomly selected voter is independent) p=0.05

The probability that X=x are independent is

P(X = x) = (?)p" (1 – p)n-1 0.05'(1 – 0.05)17-1 I = 0,1,..., 17

a) The probability that none of the people are independent is

P(X =0) = ( 1 0 .05°(1 – 0.05)17-0 17! 0!(17 - 0);0.05'(1 – 0.05) 17– = (1 -0.05) 17 = 0.4181

ans: The probability that none of the people are independent is 0.4181

b) The probability that fewer than 5 are independent is (fewer than 5 is 4 or less )

P(X<5) = P(X =0) + P(X = 1) +P(X = 2) + P(X = 3) + P(X = 4) (17)0.05°(1 – 0.05)17-0 + ... + (17)0.05*(1 – 0.05)17-4 10 (4) 17! 17! 0.05'(1 – 0.05)17-0 +...+- 0!(17 – 0)! 0.05'(1 – 0.05) 17-4 * 4!(17 – 4)! = 0.4181 +0.3741 + 0.1575 + 0.0415 +0.0076 = 0.9988

ans: The probability that fewer than 5 are independent is 0.9988

c) The probability that more than 3 are independent is (more than 3 is 4 or more  )

P(x > 3) = 1 - P(X<3) =1-(P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)) =1-((0.05°(1 – 0.05)17-0 + ... + ( 1 )0.05*(1 – 0.05)17-3 =1- (0.4181 +0.3741 +0.1575 +0.0415) = 0,0088 3

ans: The probability that more than 3 are independent is 0.0088