Question

Identify which of the following is a binomial experiment:

a) Three cards are selected from a standard 52-card deck with replacement. The number of aces selected is recorded.
b) A poll of 1200 registered voters is conducted in which the respondents are asked whether they believe Congress should reform Social Security.
c) A random sample of 15 college seniors is obtained, and the individuals selected are asked to state their ages.
d) A basketball player who makes 80% of her free throws is asked to shoot free throws until she misses. The number of free-throw attempts is recorded.
e) An experimental drug is administered to 100 randomly selected individuals with the number of individuals responding favorably recorded.

Answer 1

The scenario that represents a binomial experiment is option b) A poll of 1200 registered voters is conducted in which the respondents are asked whether they believe Congress should reform Social Security since it fulfills all the criteria of a binomial experiment.

Step-by-step explanation:

To identify which of the following is a binomial experiment, we need to consider the characteristics that define such an experiment:

1. There are a fixed number of trials, n.
2. Each trial has only two possible outcomes: success or failure.
3. The trials are independent, and the probability of success p and failure q remain constant throughout each trial.

From the given options, the one that fits all these criteria is:

b) A poll of 1200 registered voters is conducted in which the respondents are asked whether they believe Congress should reform Social Security.

This is a binomial experiment because:

• There are a fixed number of trials (1200 voters).
• There are only two possible outcomes for each trial (either the voter believes Congress should reform Social Security, or they do not).
• The trials are independent (one voter's belief does not affect another's), and the probability of either outcome remains constant for each trial.

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