• Understand the properties, characteristics, and importance of a normal distribution in statistical analysis.
• Explain how changing the mean and standard deviation will change the characteristics of a normal curve.

Normal Curve

There are many normal curves. Even though all normal curves have the same bell shape, they vary in their center and spread.

The shape of a normal curve will depend on the standard deviation.

The standard deviation, [latex]\sigma[/latex] (pronounced “sigma”), is often referred to as the scale parameter.

The shape of a normal curve will still be bell-shaped and unimodal, but the standard deviation will change how spread out or flat the curve appears.

In the following figure, all three curves have different heights and widths, but they are all still normal distributions with the same mean. As the standard deviation increases, the curve gets flatter. The standard deviation of the red curve (the tall curve) is [latex]1[/latex], the standard deviation of the blue curve (the middle curve) is [latex]2[/latex], and the standard deviation of the purple curve (the shorter curve) is [latex]3[/latex].

Let’s explore the normal curve by changing its mean ([latex]\mu[/latex]) and its standard deviation ([latex]\sigma[/latex]).

[Trouble viewing? Click to open in a new tab.]