standard deviation question

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 tbothdo to the area under the curve?

Answer 1

Hi, Emily! First, let's talk about the curve in the context of the Central Limit Theorem. The curve is centered at the population average. So, if the Standard Deviation increases, the curve will be more spread out (wider). This also means that the curve will be shorter. The opposite is true as well. The smaller the Standard Deviation is, the taller the curve will be. Both of these cases do not change the area under said curves which is always 1 (you can also think of it as the 100% of what's under the curve).

Think of it as a pile of sand. The wider you spread out the sand (bigger standard deviation), the shorter the pile will be. The narrower you bunch up the sand (smaller standard deviation), the taller the curve will be. Hope this help!