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Osbert12, Master's Degree
Category: Calculus and Above
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Experience:  Math Tutor
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# Briefly explain the main characteristics of a normal distribution.

### Customer Question

Briefly explain the main characteristics of a normal distribution. Illustrate with the help of graphs.

What are the parameters of the normal distribution?

How do the width and height of a normal distribution change when its mean remains the same but its standard deviation decreases?
Submitted: 5 years ago.
Category: Calculus and Above
Expert:  Osbert12 replied 5 years ago.

Thanks for the request.

The normal distribution is symmetric with one mode. It is a continuous distribution defined for all real values. It has a bell-shape, and it is the limiting distribution in the Central Limit Theorem.

The parameters are μ, the mean, and σ, the standard deviation.

How do the width and height of a normal distribution change when its mean remains the same but its standard deviation decreases?

The height increases. Although the total spread remains from -∞ to ∞, the width of the peaked section narrows.

Osbert

Customer: replied 5 years ago.
Do you know if there is a publicly available graph that I might find online?
Expert:  Osbert12 replied 5 years ago.

You can look up normal distribution graphs if you simply want an image of any normal distribution. If you want to graph your own normal distribution you can do that in Excel, or you can download a graphing program such as Graph 4.4.

Osbert

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Customer: replied 5 years ago.
I have a follow up. What is the narrative for these symbols, please?
-∞ to ∞,

Thanks!
Expert:  Osbert12 replied 5 years ago.

Where I wrote from -∞ to ∞ I meant the normal distribution is defined for all real values, from negative infinity (-∞) to infinity (∞).

The graphs I sent theoretically start infinitely far to the left and end infinitely far to the right. Drawing a small section of the normal distribution suffices since the normal distribution decays exponentially to zero on both sides of the mean.

Osbert