The normal distribution

Problem types

• Normal models and the 68–95–99.7 rule
• Normal model: probability between two values or count above a value

Builds on

• Describing spread and outliers
• Defining a random variable · Earlier idea

  A continuous random variable with a bell-shaped distribution is described by a mean and standard deviation.

• Comparing center, spread, and shape · Earlier idea

  Standard deviations compare spread, and the normal rule uses them to say what fraction of values lie within them.

• Dot plots, histograms, and box plots · Earlier idea

  A histogram of many values that is symmetric and bell-shaped is described by a normal distribution.

• Mean of a data set · Earlier idea

  The mean is the center of a data set, and a normal model is described by its mean and standard deviation.

Leads to

• A margin of error from simulated samples · Extend the idea

  Sample means vary in a roughly normal pattern, so the normal rule gives the margin of error for a sample size.

• Margin of error and what a sample supports · Extend the idea

  Means of repeated samples vary in a roughly normal pattern, so the same rule that gives percents within standard deviations gives the margin of error.

• A distribution from a sample space · Extend the idea

  A normal distribution is a theoretical distribution with a mean and standard deviation, as a discrete distribution has an expected value.

Related skills

None listed.