CurriculumGrade 11Mathematics

The Normal Distribution

Aligned to S-ID.A.4 — Common Core State Standards for Mathematics.

What this lesson teaches

Many data sets are bell-shaped and can be modeled by a normal distribution using the mean and standard deviation. About 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.

Worked example

Test scores have mean 70 and standard deviation 5. About what percent score between 65 and 75? That range is one standard deviation each side of the mean, so about 68% of scores fall between 65 and 75.

Practice questions

  1. With mean 100 and standard deviation 10, give the range holding the middle 95%.
  2. About what percent of data lies above the mean in a normal curve?
  3. Scores are mean 50, sd 8: estimate the percent below 42.

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

▶ Watch this lesson

En español

La Distribución Normal

Muchos conjuntos de datos tienen forma de campana y se pueden modelar con una distribución normal usando la media y la desviación estándar. Cerca del 68% de los datos cae dentro de una desviación estándar de la media, 95% dentro de dos, y 99.7% dentro de tres.

Ejemplo: Las calificaciones tienen media 70 y desviación estándar 5. ¿Aproximadamente qué porcentaje obtiene entre 65 y 75? Ese rango es una desviación estándar a cada lado de la media, así que cerca del 68% de las calificaciones cae entre 65 y 75.

More Statistics & Probability lessons

Inference from a Random SampleS-IC.A.1Comparing Two TreatmentsS-IC.B.5Events as Subsets of OutcomesS-CP.A.1Conditional ProbabilityS-CP.B.6

Teach this lesson today

An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.

Start free — no card required