Normal Distributions and the Empirical Rule
Aligned to S-ID.A.4 — Common Core State Standards for Mathematics.
What this lesson teaches
Bell-shaped data can be modeled by a normal distribution described by its mean and standard deviation. The empirical rule says about 68% of values lie within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3.
Worked example
Test scores have mean 70 and standard deviation 10. About 95% of scores fall within 2 standard deviations of the mean, that is between 70 − 20 = 50 and 70 + 20 = 90.
Practice questions
- About what percent of data lies within 1 standard deviation of the mean?
- Heights average 160 cm with a standard deviation of 5 cm. Between what values do about 68% fall?
- With mean 100 and standard deviation 15, estimate the percent of values above 130.
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Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
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Distribuciones normales y la regla empírica
Los datos con forma de campana se pueden modelar con una distribución normal descrita por su media y su desviación estándar. La regla empírica dice que cerca del 68% de los valores está dentro de 1 desviación estándar de la media, el 95% dentro de 2 y el 99.7% dentro de 3.
Ejemplo: Las calificaciones de un examen tienen media 70 y desviación estándar 10. Cerca del 95% de las calificaciones está dentro de 2 desviaciones estándar de la media, es decir entre 70 − 20 = 50 y 70 + 20 = 90.
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