Statistics question with standard deviation

Question

What happens to the curve when the standard deviation is increased? What does that do to the area under the curve? What happens to the curve when the standard deviation is decreased? What does both do to the area under the curve?

Answer 1

The area under the curve doesn't change no matter what you have for standard deviation. So area under the curve is always equal to 1. Standard deviation changes the spread, but not the total area under the curve. If you reduce the standard deviation it will be less spread curve. I hope this helps