Back to Fit data to a normal distribution — Problem 1 · Task Set 4

Exercises: Fitting Data to a Normal Distribution

Work through each section in order. For empirical-rule problems, use the 68-95-99.7 percentages and the curve's symmetry. For z-score problems, first standardize with $z = \frac{x - \text{mean}}{\text{SD}}$, then look up the area with a calculator, spreadsheet, or table. Round percentages as directed. Remember: the empirical rule and z-scores apply ONLY to roughly normal data.

Grade 10·21 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-id-a-4

Work through problems with immediate feedback

Warm-Up: The Normal Curve

These problems review the shape and vocabulary of the normal model.

$A symmetric bell curve with a single peak at the center labeled mean = median, dashed inflection lines at plus and minus one standard deviation, and tails approaching the axis.$

The diagram shows a normal (bell) curve. Which statement correctly describes its features?

It is symmetric about the mean, has a single peak at the mean (which equals the median), and its tails approach but never touch the axis.

It is symmetric, but the peak sits at the median, which is different from the mean.

It has two equal peaks, one on each side of the mean.

Its tails eventually reach and touch the horizontal axis.