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

Fluency Practice

Use the empirical rule and z-scores. Test scores below are normal with mean 500, SD 100.

$A normal curve over a test-score axis marked at 200, 300, 400, 500, 600, 700, 800, with nested bands labeled 68 percent, 95 percent, and 99.7 percent centered on the mean of 500.$

Test scores are normally distributed with mean $500$ and standard deviation $100$ . The diagram shows the empirical-rule bands. About what percentage of scores fall between $400$ and $600$ (within one standard deviation of the mean)? Enter a number (percent).