CCSS.Math.Content.HSS-ID.A.4
The standard
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
Common Core State Standards for Mathematics
What this standard means
Students need to connect a data set’s mean and standard deviation to a normal model. They should use that model to estimate percent of values in an interval, above a value, or below a value. They should also use a calculator, spreadsheet, or z-table to find normal curve areas.
Mastery looks like choosing the right tool, stating the percent in context, and checking whether a normal model makes sense. Students often get stuck using the sample data percent instead of the model percent, mixing up left and right tail areas, or applying a normal model to skewed or clearly non-bell-shaped data.
Ways to teach it
- Have students measure wrist circumferences, make a dot plot, compute mean and standard deviation, then compare actual percentages to normal model estimates.
- Ask students to explain when a normal model would be a poor fit for quiz scores, income data, or shoe sizes.
- Give one mean, standard deviation, and cutoff value, then ask students to find the percent below it using Desmos or a calculator.
- Use heights of adult women or battery life claims to discuss how companies estimate percentages without measuring every person or product.
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