Calculus and Above
Calculus Questions? Ask a Mathematician for Answers ASAP
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.
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.
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.