Question

determine whether or not the procedure described below results in a binomial distribution. if it is not binomial, identify at least one requirement that is not satisfied. 400 different voters in a region with 2 major political parties, A and B, are randomly selected from the population of 6500 voters. Each is asked if he is a member of political party A. choose the correct answer below:A. no, the trials are not independant and the sample is more than 5% of the populationB. no, there are more than two possible outcomes.C. Yes, the result is a binomial probability distributionD. no, the number of trials is not fixed.E. No, the probability of success is not the same in all trials.

Answer 1

To consider a procedure as a binomial distribution, several properties or conditions must be met:

1) each essay has two possible answers: success and failure, in addition these must be exclusive and exhaustive, in this case be of the A party (success) or not be (failure), besides nobody can be and not be of the A party (exclusive ) and these are all the possibilities that an individual has (exhaustive).

2) each trial must be independent, that is, the result of one should not affect the other, in this case the membership of each person interviewed in one party does not affect the response of the next.

3) the probability of success must be constant, in this case the probability that an individual belongs to party A (probability of success) is constant since it depends on the ratio between the number of people belonging to this party and the total voters in the region.

4) the binomial distribution counts the number of successes in a given number of trials, in this case the procedure seeks to count the successes (belonging to party A) given a number of trials (the sample of 400 voters)

Then the answer is the C. Yes, the result is a binomial probability distribution