In Problems 7–16, determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why.  
A random sample of 30 cars in a used car lot is obtained, and their mileages recorded. 

Verified step by step guidance

1. Recall the definition of a binomial experiment: it must have a fixed number of trials, each trial must be independent, each trial must have only two possible outcomes (success or failure), and the probability of success must be the same for each trial.
2. Identify the number of trials in the experiment: here, 30 cars are sampled, so there are 30 trials.
3. Check if each trial has only two possible outcomes: in this case, the mileage of each car is recorded, which is a continuous variable, not a binary outcome.
4. Determine if the trials are independent: assuming the sample is random, the mileages of different cars can be considered independent.
5. Since the outcome for each trial is not binary (success/failure), this experiment does not meet the criteria for a binomial experiment.

Key Concepts

Binomial Experiment Criteria

A binomial experiment consists of a fixed number of independent trials, each with only two possible outcomes (success or failure), and a constant probability of success across trials. Understanding these criteria helps determine if a given experiment fits the binomial model.

Independence of Trials

Independence means the outcome of one trial does not affect the outcome of another. In binomial experiments, each trial must be independent to ensure the probability of success remains constant throughout the experiment.

Nature of the Data Collected

Binomial experiments involve categorical data with two outcomes, while recording mileages is a continuous measurement. Recognizing the type of data collected is essential to decide if the experiment qualifies as binomial.