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

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

Use random sampling to draw inferences about a population.

Draw informal comparative inferences about two populations.

Calculate expected values and use them to solve problems.

Summarize and describe distributions.

Investigate patterns of association in bivariate data.

Use probability to evaluate outcomes of decisions.

Develop understanding of statistical variability.

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

Understand and evaluate random processes underlying statistical experiments.

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

Interpret linear models.

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

Use the rules of probability to compute probabilities of compound events in a uniform probability model.
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: 1