The more × an event is repeated, the more predictable the outcome becomes. This is an example of

Rationale

The more times an event is repeated, the more predictable the outcome becomes is an example of the law of large numbers.

The law of large numbers states that as the number of trials in a random experiment increases, the sample mean will converge to the expected value, leading to greater predictability in outcomes. This principle highlights the relationship between sample size and the reliability of statistical results.

A (the law of large numbers.) CORRECT

This is the correct answer as it directly relates to the principle that repeated trials lead to outcomes that approach the expected value. The law of large numbers ensures that as more data points are collected, the average of those points will likely reflect the true population average, thus enhancing predictability.

B (standard deviation.) YOUR ANSWER

Standard deviation measures the amount of variation or dispersion in a set of values. While it is related to predictability, it does not describe the process by which repetition increases predictability. Instead, it quantifies how much individual data points differ from the mean, rather than addressing the convergence of outcomes from repeated events.

C (average dispersion.) YOUR ANSWER

Average dispersion is not a standard statistical term and may refer to the spread of data points in a dataset. However, it does not convey the concept of predictability improving with increased repetition of events. The term does not directly relate to the statistical principles governing repeated trials.

D (normal variance.) YOUR ANSWER

Normal variance pertains to the variability of a normal distribution and does not address the predictability of outcomes based on repetition. This choice refers to the properties of normally distributed data rather than the statistical behavior observed when increasing the number of trials in an experiment.

Conclusion

The law of large numbers effectively illustrates how repeated trials enhance predictability by ensuring that the average outcome aligns with the expected value. In contrast, the other options focus on different aspects of statistical analysis, such as variation and distribution, which do not directly relate to the principle of predictability through repetition. Understanding this law is crucial in fields like statistics and probability, where reliable predictions are essential.

The more × an event is repeated, the more predictable the outcome becomes. This is an example of

The more times an event is repeated, the more predictable the outcome becomes is an example of the law of large numbers.

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