Question

how are the alpha level and confidence level related to the normal curve of 68/95/99- 1,2 and 3 standard deviation?

Answer 1

you can better understand with graphs:

have a closer look on the graph and it is self explained. We know that sd is measure of how much your distribution is spread out and above bell shaped curve is normal probability curve.

mu+sigma, mu+2sigma and mu+3sigma tell us how much far we are going away from the mean on the right.

similarly, mu-sigma, mu-2sigma and mu-3sigma tell the same thing on the left.

So basically we take one sigma limit ,2 sigma limit, 3 sigma limit to tell how the data is scattered within the normal curve.

The probabilities i.e 68% 95% and 99% are estimated already with the help of normal table.

SO, the prob. that data is spread out within 1 sigma limit is 68%

2 sigma limit is 95%

3 sigma limit is 99%