Select “True” if the following is an example of a binomial experiment.

Select “False” if the following is NOT an example of a binomial experiment.

A study finds that 12% of U.S. adults smoke cigarettes every day. A researcher asks 500 random adults if they smoke.

Question

Select “True” if the following is an example of a binomial experiment.

Select “False” if the following is NOT an example of a binomial experiment.

A study finds that 12% of U.S. adults smoke cigarettes every day. A researcher asks 500 random adults if they smoke.

BlackTom AI · Accepted Answer

When evaluating whether a scenario is a binomial experiment, we look for four key features: a fixed number of trials, each trial resulting in a binary outcome (success or failure), constant probability of success across trials, and independence between trials.

In this scenario, the researcher plans to ask 500 random adults a yes/no question: do you smoke? The trial count is fixed at n = 500, satisfying the fixed-number requirement.

Each trial yields a binary outcome: the respondent either smokes (a 'success' for the event of interest) or does not smoke (a 'failure').

If we treat the population proportion as p = 0.12 (12%), each trial has a constant probability of yielding a 'smoker' response, assuming sampling is representative and questions are asked consistently.

Independence is typically assumed in such surveys when sampling is random, especially with a large population relative to the sample size; the outcome of one respondent does not practically dictate the outcome of another, making trials approximately independent.

Given these conditions—fixed number of trials, binary outcomes, constant probability, and independence—the situation aligns with a binomial (Bernoulli) framework.

BU-STAT-2103-750-49509-202503 Quiz 3

Select “True” if the following is an example of a binomial experiment. Select “False” if the following is NOT an example of a binomial experiment. A study finds that 12% of U.S. adults smoke cigarettes every day. A researcher asks 500 random adults if they smoke.

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