Final answer:
The situations of tossing a coin, rolling a die, drawing a card (with replacement), and measuring students' heights can all be considered binomial experiments if they adhere to the criteria of a fixed number of trials, binary outcomes, and independent and identical conditions for each trial.
Step-by-step explanation:
A binomial experiment is a statistical experiment that meets the following three criteria: there is a fixed number of trials (n), there are only two possible outcomes (success and failure), and the trials are independent of each other, with the probability of success (p) and failure (q) being the same for each trial. Given this definition, let's evaluate the provided situations.
- Tossing a coin 60 times and recording the number of times it lands on heads does qualify as a binomial experiment. The fixed number of trials is 60, the outcome is binary (heads or tails), and each toss is independent with consistent probabilities of success and failure.
- Rolling a fair six-sided die and recording the number of times it lands on a 3 qualifies as a binomial experiment. There are a fixed number of rolls, the outcome is binary (a 3 or not a 3), and each roll is independent with consistent probabilities.
- Drawing a card from a standard deck of 52 cards and recording whether it is a heart qualifies as a binomial experiment if the card is replaced after each draw. Without replacement, it would not meet the criteria of identical conditions for each trial.
- Measuring the height of 100 selected students and recording whether they are taller than 6 feet is also a binomial experiment. The fixed number of trials is 100, the outcome is binary (taller than 6 feet or not), and each measurement is independent with consistent probabilities.
All the provided situations, when following the replacements for cards, can be classified as binomial experiments because they adhere to the necessary criteria of fixed number of trials, two possible outcomes, and independence of trials.