Question

Which of the following are binomial distribution studies? Select all that apply.

A) The probability that a voter is a lobbyist.
B) The probability that a voter voted in another state last year.
C) The probability of five out of ten individuals voting no on a proposal.
D) The probability of a political candidate getting campaign contributions from a specific organization.
E) The probability of three out of nine individuals voting yes on a mill levy.

Answer 1

Only options (C) and (E) clearly meet the criteria for a binomial distribution, as they both involve a fixed number of trials with two possible outcomes per trial and the assumption of independence between trials.

Step-by-step explanation:

To determine which of the given scenarios could be modeled by a binomial distribution, we need to consider whether each scenario meets the criteria of the binomial distribution. The key characteristics include:
1. The number of trials is fixed.
2. Each trial has only two possible outcomes (success or failure).
3. The probability of success is the same for each trial.
4. The trials are independent of each other.

Considering these characteristics:

• (C) The probability of five out of ten individuals voting no on a proposal falls under the binomial distribution because it involves a fixed number of trials (10 individuals), two possible outcomes (vote no or not), constant probability (assuming it's the same for each individual), and each person's vote is independent.
• (E) The probability of three out of nine individuals voting yes on a mill levy is also a binomial distribution for the same reasons as option (C).

The other options do not clearly define the number of trials or the probability of success, making it difficult to classify them definitively as binomial distribution scenarios without additional information.