options: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Calculate expected values and use them to solve problems.

Interpret linear models.

Develop understanding of statistical variability.

Summarize, represent, and interpret data on a single count or measurement variable.

Draw informal comparative inferences about two populations.

Investigate chance processes and develop, use, and evaluate probability models.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Summarize and describe distributions.

Use random sampling to draw inferences about a population.

Understand and evaluate random processes underlying statistical experiments.

Use probability to evaluate outcomes of decisions.

Understand independence and conditional probability and use them to interpret data.

Investigate patterns of association in bivariate data.
problem_activity: Task
The half-life of Carbon $14$, that is, the time required for half of the Carbon $14$ in a sample to decay, is variable: not every Carbon $14$ specimen has exactly the same half life. The half-life for Carbon $14$ has a distribution that is approximately normal with a standard deviation of $40$ years. This explains why the Wikipedia article on Carbon $14$ lists the half-life of Carbon 14 as $5730 \pm 40$ years. Other resources report this half-life as the absolute amounts of $5730$ years, or sometimes simply $5700$ years.
Explain the meaning of these three quantities ($5730 \pm 40$, $5730$, and $5700$) focusing on how they differ.
Can all three of the reported half-lives for Carbon $14$ be correct? Explain.
What are some of the benefits and drawbacks for each of the three ways of describing the half-life of Carbon $14$?


correct_option_index: 4