Question

dialsd-algebra ii, s2-rang
pre-test complete
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forty-four percent of the members of the science club wear blue shirts. which of the following is a binomial experiment?
selecting eight members randomly and recording whether each member is wearing a blue shirt
selecting eight members randomly and recording the number in the group wearing a blue shirt
selecting members randomly until one without a blue shirt is chosen
selecting members randomly until one with a blue shirt is chosen

Explanation:

A binomial experiment has 4 key traits: a fixed number of independent trials, each trial has 2 outcomes (success/failure), constant probability of success, and we count successes.

1. The first option has 8 fixed trials, each trial (member check) has 2 outcomes (blue shirt/ not blue shirt), constant 44% success probability, and records each trial's outcome (which fits binomial criteria).
2. The second option counts total successes in fixed trials but is a hypergeometric scenario if sampling without replacement, and does not record individual trial binary outcomes as required for binomial experiment definition here.
3. The third and fourth options have no fixed number of trials (they stop at a specific outcome), so they do not meet binomial requirements.

Answer:

A. Selecting eight members randomly and recording whether each member is wearing a blue shirt